Chapter 6: Percents

42430_Cleaves_ch06 4/12/04 1:22 PM Page 172 

Profit • Loss • Cash • Checking Account 

W ages • Gross Pay • Payroll • Payroll Tax 

Sales Tax • Property Tax • Income Tax 

Insurance • Credit • Loan • Bank Statement 

Net Price • List Price • Trade Discount 

Cash Discount • Markup • Markdown 

Simple Interest • Compound Interest 

Chapter 

Promissory Notes • Present Value 

6 

Future Value • Annuity • Sinking Funds 

Investments • Stocks • Bonds • Depreciation 

Inventory • Turnover • Overhead • Mortgage 

Measurement • Distribution • Ratios 

Financial Statement • Balance Sheet 

Operating Income • Gross Margin 

Accounts Receivable • Assets • Liabilities 

Capital • Equity • Cost of Goods


Insurance • Credit • Loan • Bank Statement 

Percents 

Net Price • List Price • Trade Discount 

Cash Discount • Markup • Markdown 

Buy a Coke—Get a Cool Cell Phone Jingle! 

Coca-Cola reported $5,054 million net operating revenues in Asia in 2002, up from $4,861 million in 2001.The increase in 

sales is impressive when you consider the conditions. In Japan, where Coca-Cola makes 27% of its Asian sales, the economy 

has been sluggish, grocery store price competition has been fierce, and vending machine sales are declining.The vending 

machine share of total beverage sales decreased from 36% in 1995 to 32% in 2003, while the supermarket sales portion of 

total beverage sales grew from 24% to 28% in the same time period. Coca-Cola’s under-30 target market is slowly aging and 

50% of Japan’s population will be over 50 by 2025.To combat these trends and keep sales strong, Coca-Cola has introduced 

the Cmode wireless vending machine in Japan. Cmode machines allow users to purchase or obtain free coupons, maps, and 

tickets printed by the printer in the vending machine, pay cash into the user’s Cmode account, obtain reward points for 

purchases, and download a variety of information into the user’s mobile phone.A strategy aimed at young consumers offers 

a Coca-Cola jingle download for a cell phone tone with the purchase of a beverage. So far, this promotional strategy has 

proved successful in increasing vending machine sales in Japan. Do you think the Cmode vending machine can be a hit in 

the United States? If 27% of Coca-Cola’s Asian sales are in Japan, how many dollars is that? What is the percentage decrease 

in vending machine sales from 1995 to 2003? 

Sources: 

1.“Coke Lures Japanese Customers with Cellphone Come-Ons,” Wall Street Journal, Monday, September 8, 2003, p. B1. 

2. www2.coca-cola.com/investors/annualreport/2002. 

Learning Outcomes 

6-1 Percent Equivalents 

1. Write a whole number, fraction, or decimal as a 

percent. 

2. Write a percent as a whole number, fraction, or 

decimal. 

6-2 Solving Percentage Problems 

1. Identify the rate, base, and portion in percent 

problems. 

2. Use the percentage formula to find the unknown value 

when two values are known. 

6-3 Increases and Decreases 

1. Find the amount of increase or decease in percent 

problems. 

2. Find the new amount directly in percent problems. 

3. Find the rate or the base in increase or decrease 

problems.


6-1 Percent Equivalents 

 


1 Write a whole number, fraction, or decimal as a percent. 

2 Write a percent as a whole number, fraction, or decimal. 

Percent: a standardized way of 

expressing quantities in relation to a 

standard unit of 100 (hundredth, per 100, 

out of 100, over 100). 

With fractions and decimals, we compare only like quantities, that is, fractions with common denominators 

and decimals with the same number of decimal places. We can standardize our representation 

of quantities so that they can be more easily compared. We standardize by expressing 

quantities in relation to a standard unit of 100. This relationship, called a percent, is used to solve 

many different types of business problems. 

The word percent means hundredths or out of 100 or per 100 or over 100 (in a fraction). That 

is, 44 percent means 44 hundredths, or 44 out of 100, or 44 per 100, or 44 over 100. We can write 

44 

44 hundredths as 0.44 or 

100. 

The symbol for percent is %. You can write 44 percent using the percent symbol: 44%; using 

fractional notation: ; or using decimal notation: 

44 

0.44. 

100 

44% = 44 percent = 44 hundredths = 44 = 0. 

44 

100 

mixed percents: percents with mixed 

numbers. 

Percents can contain whole numbers, decimals, fractions, mixed numbers, or mixed decimals. 

Percents with mixed numbers and mixed decimals are often referred to as mixed percents. 

Examples are 33 %, 0. 05 %, and 023 . 1 3 

%. 

1 

3 

3 

4 

1 

 

Write a whole number, fraction, or decimal as a percent. 

The businessperson must be able to write whole numbers, decimals, or fractions as percents, and 

to write percents as whole numbers, decimals, or fractions. First we examine writing whole numbers, 

decimals, and fractions as percents. 

Hundredths and percent have the same meaning: per hundred. Just as 100 cents is the same 

as 1 dollar, 100 percent is the same as 1 whole quantity. 

100% 1 

This fact is used to write percent equivalents of numbers, and to write numerical equivalents of 

percents. It is also used to calculate markups, markdowns, discounts, and numerous other business 

applications. 

When we multiply a number by 1, the product has the same value as the original number. 

N 1 N. We have used this concept to change a fraction to an equivalent fraction with a higher 

denominator. For example, 

2 1 2 

1 = and × = 

2 2 2 

We can also use the fact that N 1 N to change numbers to equivalent percents. 

2 

4 

Points to Stress 

N 

, and 

N = 1 100 = 1 

N 1 N are mathematical concepts 

that are often used to change the form of 

a value. It is important to understand that 

the value is not changed by multiplying 

by 100%. 

1 1 100% 

1 = 100% × 100% 

= × = 50% 

2 2 1 

05 . × 100% = 050.% = 50% 

In each case when we multiply by 1 in some form, the value of the product is equivalent to 

the value of the original number even though the product looks different. 

1 

50 

, % Write 0.3 as a percent. 

How To 

Write a number as its percent equivalent 

1. Multiply the number by 1 in the form of 100%. 

2. The product has a % symbol. 

0.3 0.3 100% 

030.% 30% 

174 Chapter 6


Ti p 

Multiplying by 1 in the Form of 100% 

To write a number as its percent equivalent, identify the number as a fraction, whole number, 

100% 

or decimal. If the number is a fraction, multiply it by 1 in the form of 1 

. If the number is 

a whole number or decimal, multiply by 100% by using the shortcut rule for multiplying by 

100. In each case, the percent equivalent will be expressed with a percent symbol. 

EXAMPLE Write the decimal or whole number as a percent. 

(a) 0.27 (b) 0.875 (c) 1.73 (d) 0.004 (e) 2 

(a) 0.27 0.27 100% 027.% 27% 

0.27 as a percent is 27%. 

(b) 0.875 0.875 100% 087.5% 87.5% 

0.875 as a percent is 87.5%. 

(c) 1.73 1.73 100% 173.% 173% 

1.73 as a percent is 173%. 

(d) 0.004 0.004 100% 000.4% 0.4% 

0.004 as a percent is 0.4% 

(e) 2 2 100% 200.% 200% 

2 as a percent is 200%. 

Multiply 0.27 by 100% (move the 

decimal point two places to the right). 







Multiply 2 by 100% (move the 


As you can see, the procedure is the same regardless of the number of decimal places in the 

number and regardless of whether the number is greater than, equal to, or less than 1. 

EXAMPLE Write the fraction as a percent. 

67 1 

7 2 

(a) (b) (c) 3 1 (d) (e) 

100 4 2 4 3 

1 

67 67 100% 

(a) = × = 67% Reduce and multiply. 

100 100 1 

(b) 

(c) 3 1 2 

(d) 

(e) 

1 

4 

7 

4 

2 

3 

25 

1 100% 

= × = 25 % 

4 1 

1 

3 1 100% 

7 100% 

= × = × = 350% 

2 1 2 1 

7 100% 

= × = 175% 

4 1 

1 

1 

25 

2 100% 200% 2 

= × = = 66 

3 1 3 3 % 

1 

50 

Reduce and multiply. 

Change to an improper fraction, reduce, 

and multiply. 

Reduce and multiply. 

Multiply. 

STOP and Check 

Write the decimal or whole number as a percent. 

1. 0.82 

2. 3.45 

82% 

345% 

Write the fraction as a percent. 

43 

3 

5. 

6. 

100 

10 

43% 

30% 

3. 0.0007 

0.07% 

7. 

8 1 4 

825% 

4. 5 

500% 

8. 

1 

6 

16 2 3 % 

Percents 175


2 

 

Write a percent as a whole number, fraction, or decimal. 

When a number is divided by 1, the quotient has the same value as the original number. N 1 

N 

N or N. We have used this concept to reduce fractions. For example, 

1 = 

We can also use the fact that N 1 N or 

2 2 2 

1 = ÷ = 

2 4 2 

N 

1 = 

1 

2 

50% 

50 

50% ÷ 100% 

= = = 

100% 

100 

50% ÷ 100% = 50 ÷ 100 = 0. 50 = 0. 

5 

N to change percents to numerical equivalents. 

1 

2 

How To 

Write a percent as a number 

1. Divide by 1 in the form of 100% or multiply by 100% . 

2. The quotient does not have a % symbol. 

1 

EXAMPLE Write the percent as a decimal. 

(a) 37% (b) 26.5% (c) 127% (d) 7% (e) 0.9% (f) 2 19 (g) 167 1 20 % 

3 % 

Points to Stress 

Remind students that dividing by 100 is 

the same as multiplying by 

1 

100 

. 

30 3 

30 ÷ 100 = = 

100 10 

1 30 1 30 3 

30 × = × = = 

100 1 100 100 10 

(a) 37% 37% 100% .37 0.37 

(b) 26.5% 26.5% 100% .265 0.265 

(c) 127% 127% 100% 1.27 1.27 

(d) 7% 7% 100% .07 0.07 

(e) 0.9% 0.9% 100% .009 0.009 

(f) 2 19 % = 295 . % ÷ 100% = . 0295 = 0.0295 

20 

(g) 167 1 % = 167. 33% ÷ 100% 

3 

= 1. 

6733 = 1.6733 or 1.673 ( rounded) 

Divide by 100 mentally. 





Write the mixed number in front of 

the percent symbol as a mixed 

decimal before dividing by 100%. 

Write the mixed number in front of 

the percent symbol as a repeating 

mixed decimal before dividing by 100. 

Ti p 

What Happens to the % (Percent) Sign? 

Division is the same as multiplying by the reciprocal of the divisor. Similarly, % . In 

% = 1 

multiplying fractions we reduce or cancel common factors from a numerator to a 

denominator. Percent signs and other types of labels also cancel. 

% ÷ % = % 1 

× = 1 

1 % 

176 Chapter 6 

EXAMPLE Write the percent as a fraction or mixed number. 

(a) 65% (b) (c) 250% (d) 83 1 3 % (e) 12.5% 

(a) 

(b) 

65 % 1 

65% = 65% ÷ 100% 

= × = 13 

1 100 % 20 

1 

4 

1 

4 

% 

1 

1% 

1 

% = % ÷ 100% 

= × = 1 

4 

4 100% 

400 

13 

250 % 1 5 

(c) 250% = 250% ÷ 100% 

= × = = 2 1 1 100 % 2 2 

5 

20 

2 

Convert division to multiplication.


(d) 83 1 83 1 250 % 1 

% = % ÷ 100% 

= × = 5 3 3 

3 100 % 6 

(e) 12 5 12 1 12 1 25 % 1 

. % = % = % ÷ 100% 

= × = 1 2 2 

2 100 % 8 

5 

1 

2 

4 

Convert to improper fraction. 

Convert mixed decimal to 

mixed number. 


Write the percent as a decimal. 

1. 52% 

0.52 

2. 38.5% 

0.385 

3. 143% 

1.43 

4. 0.72% 

0.0072 

Write the percent as a fraction or mixed number. 

5. 72% 

18 

25 

6. 

1 

% 

8 

7. 325% 

1 

800 

3 1 4 

8. 

16 2 3 % 

1 

6 

6-1 Section Exercises 

Skill Builders 

Write the decimal as a percent. 

1. 0.39 

0.39 0.39 100% 39% 

2. 0.693 

0.693 0.693 100% 69.3% 

3. 0.75 

0.75 0.75 100% 75% 

4. 0.2 

0.2 0.2 100% 20% 

5. 2.92 

2.92 2.92 100% 292% 

6. 0.0007 

0.0007 0.0007 100% 0.07% 

Write the fraction as a percent. 

7. 

39 

100 

39 

100 

39 100 % 

= × = 39% 

100 1 

1 

1 

8. 

3 

4 

3 100 % 

× = 75% 

4 1 

1 

25 

9. 

3 2 5 

3 2 20 

17 100 % 

= × = 340% 

5 5 1 

1 

10. 

5 1 4 

5 1 4 

21 100 % 

= × = 525% 

4 1 

1 

25 

11. 

9 

4 

9 

4 

9 100 % 

= × = 

4 1 

1 

25 

225% 

12. 

7 

5 

7 100 % 

× = 140% 

5 1 

1 

20 

13. 

2 

300 

2 100 % 

× = 

300 1 

3 

1 

2 

3 

% 



Write the percent as a decimal. Round to the nearest thousandth if the division does not terminate. 

14. 

15 1 2 % 15. 1 

8 % 

15 1 % = 15. 5% 

2 

) 0 . 125 

81000 . 

= 15.% 5 ÷ 100% = 0. 

155 

8 

20 

16 

40 

40 

1 

% = 0. 125% = 0. 125% ÷ 100% 

8 

= 0. 

00125 

16. 45% 

45% 100% 0.45 

17. 150% 

150% 100% 1.5 

18. 

125 1 3 % 19. 3 

7 % 

125 1 % = 125. 3% 

3 

) 0.428 

7 3.000 

= 125. 3% ÷ 100% 

28 

= 1. 253 ( rounded) 

20 

14 

60 

56 

4 

3 

% = 0. 428% ÷ 100% = 0. 

004 

7 

(rounded) 

Write the percent as a fraction. 

20. 45% 

45% 

9 

45% 

= = 

100% 

20 

21. 60% 

60% 

100% = 

3 

5 

22. 250% 

23. 180% 

250% 

5 

2 1 100% = 2 

= 180% 

18 9 

180% 

= = = = 1 4 

2 

100% 

10 5 5 

24. 

3 

33 1 3 % 

4 % 25. 3 3 

3 1 3 

% = % ÷ 100% = % × = 

33 1 33 1 100 33 1 1 

% = % ÷ % = % × 

4 4 

4 100% 

400 

3 3 

3 100% 

1 

100 1 1 

= × = 

3 100 3 

1 

Formula: a relationship among quantities 

expressed in words or numbers and 

letters. 

Base: the original number or one entire 

quantity. 

Percentage: a part or portion of the base. 

Portion: another term for percentage. 

Rate: how the base and percentage are 

related expressed as a percent. 

6-2 Solving Percentage Problems 


1 Identify the rate, base, and portion in percent problems. 

2 Use the percentage formula to find the unknown value when two values are known. 

1 

 

Identify the rate, base, and percentage in percent problems. 

A formula expresses a relationship among quantities. When you use the five-step problemsolving 

approach, the third step, the Solution Plan, is a formula written in words and letters. 

The percentage formula, Percentage Rate Base, can be written as P R B or P RB. 

The letters or words represent numbers. When the numbers are put in place of the letters, the formula 

guides you through the calculations. 

In the formula P R B, the base (B) represents the original number or one entire quantity. 

The percentage (P) represents a portion of the base. The rate (R) is a percent that tells us 



how the base and portion are related. In the statement “50 is 20% of 250,” 250 is the base (the entire 

quantity), 50 is the portion (part), and 20% is the rate (percent). 

How To 

Identify the rate, base, and portion. 

1. Identify the rate. Rate is usually written as a percent, but it may be a decimal or fraction. 

2. Identify the base. Base is the total amount, original amount, or entire amount. The base is 

often closely associated with the preposition of. 

3. Identify the portion. Portion can refer to the part, partial amount, amount of increase or 

decrease, or amount of change. It is a portion of the base. The portion is often closely 

associated with a form of the verb is. 

EXAMPLE Identify the given and missing elements for 

(a) 20% of 75 is what number? 

(b) What percent of 50 is 30? 

(c) Eight is 10% of what number? 

R B P 

Use the identifying key words for rate (percent or %), 


base (total, original, associated with the word of ), 

Percent Total Part 

and portion (part, associated with the word is). 

R B P 

(b) What percent of 50 is 30? 

Percent Total Part 

P R B 

(c) Eight is 10% of what number? 

Part Percent Total 


Identify the base, rate, and portion. 

1. 42% of 85 is what number? 

Base, 85; rate, 42%; portion, not known 

3. What percent of 80 is 20? 

Base, 80; rate, not known; portion, 20 

2. Fifty is 15% of what number? 

Base, not known; rate, 15%; portion, 50 

4. Twenty percent of what number is 17? 

Base, not known; rate, 20%; portion, 17 

5. Find 125% of 72. 

Base, 72; rate, 125%; portion, not known 

2 

Use the percentage formula to find the unknown value when 

two values are known. 

The percentage formula, Percentage Rate Base, can be written as P R B. Another word 

for percentage is portion. The letters or words represent numbers. When the numbers are put in 

place of the letters, the formula guides you through the calculations. 

The three percentage formulas are 

Percentage = Rate × Base P = R × B For finding the percentage or portion. 

Percentage 

P 

Base = B = For finding the base. 

Rate 

R 

Percentage 

P 

Rate = R = For finding the rate. 

Base 

B 

Circles can help us visualize these formulas. The shaded part of the circle in Fig. 6-1 represents 

the missing amount. The unshaded parts represent the known amounts. If the unshaded parts 



P R × B 

B P R 

R P B 

P 

P 

P 

R B 

R B 

R 

B 

FIGURE 6-1 

are side by side, multiply their corresponding numbers to find the missing number. If the unshaded 

parts are one on top of the other, divide the corresponding numbers to find the missing number. 

How To 

Use the percentage formula to solve percentage problems 

1. Identify and classify the two known values and the one missing value. 

2. Choose the appropriate percentage formula for finding the missing value. 

3. Substitute the known values into the formula. For the rate, use the decimal or fractional 

equivalent of the percent. 

4. Perform the calculation indicated by the formula. 

5. Interpret the result. If finding the rate, convert decimal or fractional equivalents of the rate 

to a percent. 

EXAMPLE Solve the problems 


(b) 20% of what number is 80? 

(c) 80 is what percent of 400? 

(a) 20% Rate 

Identify known values and missing value. 

400 Base 

Portion is missing 

P = R × B 

Choose the appropriate formula. 

P = 02 . × 400 

Substitute values using the decimal equivalent of 20%. 

P = 80 

Perform calculation. 

20 % of 400 is 80. 

Interpret result. 

(b) 20% Rate 


80 Portion 

Base is missing 

P 

B = 


R 

80 

B = 

Substitute values. 

02 . 

B = 400 

20 % of 400 is 80. 

(c) 80 Portion 

400 Base 

Rate is missing 

P 

R = 

B 

80 

R = 

400 

R = 02 . or 20% 

80 is 20% of 400. 


Interpret result. 



Substitute values. 


Interpret result. 0.2 20%. 

Very few percentage problems that you encounter in business tell you the values of P, R, and 

B directly. Percentage problems are usually written in words that must be interpreted before you 

can tell which form of the percentage formula you should use. 



formula that is to be used. 

300 

2 900 

Teaching Tip 

P = × = 600 The rate is 3 

; the base is 900. Write 66 2 3 as a fraction. 

3 1 

% 

% 

In the example, discuss the effect that 

rounding 66 2 3 % 1 

Multiply 

to 0.67 or 0.6667 has 

EXAMPLE During a special one-day sale, 600 customers bought the on-sale pizza. Of 

these customers, 20% used coupons. The manager will run the sale again 

the next day if more than 100 coupons were used. Should she run the sale 

again? 

What You Know What You Are Looking For Solution Plan 

Total customers: 600 Quantity of coupon-using The quantity of coupon- 

Coupon-using customers as customers using customers is a 

P 

a percent of total Should the manager run the portion of the base of 

customers: 20% sale again? total customers, at a rate of 

20% (Figure 6-2). 

R 

20% 

B 

600 

P R B 

Quantity of coupon-using 

customers R B 

FIGURE 6-2 

Solution 

Teaching Tip 

P = R × B 

P is missing 

In the example, have students write R 

R 20% 

above 20% and B above 600. They 

B 600 

should also underline the question, 

P = 20% 

× 600 

Substitute known values. Change % to decimal equivalent. 

“Should she run the sale again?” 

P = 02 . × 600 

Multiply. 

P = 120 

Conclusion 

The quantity of coupon-using customers is 120. 

Since 120 is more than 100, the manager should run the sale again. 

EXAMPLE If 66 2 3 % of the 900 employees in a company choose the Preferred 

Provider insurance plan, how many people from that company are enrolled 

in the plan? 

First, identify the terms. The rate is the percent, and the base is the total number of employees. 

The portion is the quantity of employees enrolled in the plan. 

Point to Stress 

To avoid a calculation error and to allow 

themselves to check their work, students P = R × B 

The portion is the unknown. 

should always write the known 

quantities in the problem and the 

P = 66 2 % × 900 

3 

on the result. 

Teaching Tip 

A drawing or diagram with the known 

values placed in the appropriate areas 

will help ensure that the correct 

computations are being done and will 

also help some students overcome their 

anxiety with word problems. 

Ti p 

Continuous Sequence Versus Noncontinuous Sequence 

We can write the fractional equivalent of the percent as a rounded decimal and divide using a 

calculator. 

AC 2 ÷ 3 = ⇒ 0.666666666 

AC 900 × .666666666 = ⇒ 599.9999994 

As one continuous sequence using the memory keys, enter 

AC 2 ÷ 3 × 900 = ⇒ 600 

Note slight discrepancies due to rounding. However, the answer obtained by using a 

continuous sequence of steps is more accurate. 

EXAMPLE Stan sets aside 15% of his weekly income for rent. If he sets aside $75 

each week, what is his weekly income? 



Identify the terms: The rate is the number written as a percent, 15%. The portion is given, $75; it 

is a portion of his weekly income, the unknown base. 

R 

15% 

P 

$75 

B 

P 

B = 

R 

$ 75 

B = 

15% 

75 

B = 

015 . 

B = $ 500 

The rate is 15% and the portion is $75 (Figure 6-3). 

The base is the weekly income to be found. 

Convert 15% to a decimal equivalent. 

Divide. 

Stan’s weekly income is $500. 

FIGURE 6-3 

EXAMPLE 

If 20 cars were sold from a lot that had 50 cars, what percent of the cars 

were sold? 

R 

P 

20 

B 

50 

P 

R = 

B 

20 

R = 

50 

20 

R = × 

50 

R = % 

100 

1 

40 1 2 

% 

Of the cars on the lot, 40% were sold. 

The portion is 20; the base is 50 (Figure 6-4). 

The rate is the unknown to find. 

Divide. 

Convert to a percent equivalent. 

FIGURE 6-4 

Teaching Tip 

Encourage students to understand these 

relationships between percent and number 

equivalents. When the percent is less than 

1%, the number equivalent is less than 

1 

100 

. When the percent is between 1% 

and 100%, the number equivalent is a 

1 

fraction between 100 and 1. When the 

percent is more than 100%, the number 

equivalent is more than 1. 

Many students mistakenly think that the portion can never be larger than the base. The portion 

(percentage) is smaller than the base only when the rate is less than 100%. The portion is 

larger than the base when the rate is larger than 100%. 

EXAMPLE 48 is what percent of 24? 

P 

R = 

B 

48 

R = 

24 

R = 2 

R = 200% 

The rate is unknown. The percentage is 48. The base is 24. 

Divide. 

Rate written as a whole number. 

Rate written as a percent. 



30 

2. 25% of what number is 120? 

480 

3. 150 is what percent of 750? 

20% 

4. Find 12 1 2 

% of 64. 

5. Seventy-five percent of students in a class of 40 passed the 

first test. How many passed? 

8 

30 





rate (%) 48% 

base (of) 12 

portion (is) missing number 

3. What percent of 158 is 47.4? 

rate (%) missing number 

base (of) 158 

portion (is) 47.4 

182 Chapter 6 


rate (%) 32% 

base (of) missing number 

portion (is) 28 

4. What number is 130% of 149? 

rate (%) 130% 

base (of) 149 

portion (is) missing number


Use the appropriate form of the percentage formula. 

5. Find P if R 25% and B 300. 

P = R × B 

P = 25% 

× 300 

P = 025 . × 300 

P = 75 

6. Find 40% of 160. 

P = R × B 

P = 40% 

× 160 

P = 040 . × 160 

P = 64 

7. What number is 33 1 3 

% of 150? 

8. What number is 154% of 30? 

P = R × B = 33 1 50 

P R B 154% 30 1.54 30 46.2 

1 150 

% × 150 = × = 50 

3 

3 1 

1 

9. Find B if P 36 and R = 66 2 3 

% 10. Find R if P 70 and B 280. 

18 

1 25 

P 36 36 36 2 36 3 

B = = = = 

R 

66 2 = × = 54 

R 

2 

% 

1 3 1 2 

= P 

B 

= 70 

= 70 

× 100 % 

280 280 1 

= 25% 

1 

3 3 


P = R × B 

P = 04 . × 30 

P = 12 

4 

1 

12. 52% of 17.8 is what number? 

P = R × B 

P = 052 . × 178 . 

P = 9. 

256 


P 

B = 

R 

21 

B = 

03 . 

B = 70 


P 

R = 

B 

4 

R = 

16 

1 

R = 

4 

R = 025 . × 100% 

R = 25% 

18. 0.8% of 50 is what number? 

P = R × B 

P = 0. 008( 50) 

P = 04 . 


P 

R = 

B 

30 

R = 

50 

3 

R = 

5 

R = 06 . × 100% 

R = 60% 

19. What percent of 15.2 is 12.7? Round 

to the nearest hundredth of a percent. 

P 

R = 

B 

12. 

7 

R = 

15. 

2 

R = 0. 835526315 × 100% 

R = 83. 55% (rounded) 

14. 17.5% of what number is 18? Round to hundredths. 

P 

B = 

R 

18 

B = 

0. 

175 

B = 102. 

86 (rounded) 


P = R × B 

P = 172 . ( 50) 

P = 86 

20. What percent of 73 is 120? Round to 

the nearest hundredth of a percent. 

P 

R = 

B 

120 

R = 

73 

R = 1. 643835616 × 100% 

R = 164. 38% (rounded) 

21. 0.28% of what number is 12? Round to the nearest 

hundredth. 

P 

B = 

R 

12 

B = 

0. 

0028 

B = 4, 285. 

71 (rounded) 

Applications 

23. At the Evans Formal Wear department store, all suits are 

reduced 20% from the retail price. If Charles Stewart 

purchased a suit that originally retailed for $258.30, how 

much did he save? 

P R B 20% $258.30 0.2 $258.30 

$51.66 saved 

22. 1.5% of what number is 20? Round to the nearest 

hundredth. 

P 

B = 

R 

20 

B = 

0. 

015 

B = 1, 333. 

33 

24. Joe Passarelli earns $8.67 per hour working for Dracken 

International. If Joe earns a merit raise of 12%, how much 

was his raise? 

P R B 12% $8.67 0.12 $8.67 $1.04 raise 



25. An ice cream truck began its daily route with 95 gallons of 

ice cream. The truck driver sold 78% of the ice cream. How 

many gallons of ice cream were sold? 

P R B 78% 95 0.78 95 74.1 gallons or 

74 gallons (rounded) 

27. A stockholder sold her shares and made a profit of $1,466. 

If this is a profit of 23%, how much were the shares worth 

when she originally purchased them? 

P 

B = R 

= $, 1 466 

% 

= $, 1 466 

. 

= $ 6, 373. 

91 original cost 

23 023 

29. Ali gave correct answers to 23 of the 25 questions on the 

driving test. What percent of the questions did he get 

correct? 

4 

P 

R = B 

= 23 

= 23 

25 25 

× 100 % 

1 

= 92% 

1 

31. Holly Hobbs purchased a magazine at the Atlanta airport 

for $2.99. The tax on the purchase was $0.18. What is the 

tax rate at the Atlanta airport? Round to the nearest percent. 

P 

R = 

B 

018 . 

R = 

299 . 

R = 0. 060200668 × 100% 

R = 6% (rounded) 

26. Stacy Bauer sold 80% of the tie-dyed T-shirts she took to 

the Green Valley Music Festival. If she sold 42 shirts, how 

many shirts did she take? 

P 

B = R 

= 42 

= 42 

80 08 

= 52.,or 5 53 shirts 

% . 

28. The Drammelonnie Department Store sold 30% of its shirts 

in stock. If the department store sold 267 shirts, how many 

shirts did the store have in stock? 

P 

B = R 

= 267 

= 267 

30% 03 . 

= 890 shirts 

30. A soccer stadium in Manchester, England, has a capacity of 

78,753 seats. If 67,388 seats were filled, what percent of 

the stadium seats were vacant? Round to the nearest 

hundredth of a percent. 

78, 753 − 67, 388 = 11, 

365 (number vacant) 

P 11, 

365 11, 

365 100% 

R = = = × 

B 78, 

753 78, 

753 1 

1, 136, 

500 

= % = 14. 43% 

vacant seats (rounded) 

78, 

753 

32. A receipt from Wal-Mart in Memphis showed $4.69 tax on 

a subtotal of $53.63. What is the tax rate? Round to the 

nearest tenth percent. 

P 

R = 

B 

$. 469 

R = 

R 

R 

$ 53. 

63 

= 0. 087451053 × 100% 

= 875 . (rounded) 

6-3 Increases and Decreases 

 


1 Find the amount of increase or decrease in percent problems. 

2 Find the new amount directly in percent problems. 

3 Find the rate or the base in increase or decrease problems. 

New amount: the ending amount after an 

amount has changed (increased or 

decreased). 

How To 

In many business applications an original amount is increased or decreased to give a new amount. 

Some examples of increases are the sales tax on a purchase, the raise in a salary, and the markup 

on a wholesale price. Some examples of decreases are the deductions on your paycheck and the 

markdown or the discount on an item for sale. 

1 

 

Find the amount of increase or decrease in percent problems. 

The amount of increase or decrease is the amount that a number changes. Subtraction is used to 

find the amount of change when the beginning and ending (or new) amounts are known. 

Find the amount of increase or decrease from the beginning and ending amounts 

1. To find the amount of increase: 

Amount of increase new amount beginning amount 

2. To find the amount of decrease: 

Amount of decrease beginning amount new amount 

EXAMPLE 

David Spear’s salary increased from $58,240 to $63,190. What is the 

amount of increase? 



Beginning amount = $ 58, 

240 

New amount = $ 63, 

190 

Increase = beginning amount − new amount 

= $ 63, 190 − $ 58, 

240 

= $ 4, 

950 

David’s salary increase was $4,950. 

Percent of change: the percent by which 

a beginning amount has changed 

(increased or decreased). 

How To 

EXAMPLE 

A coat was marked down from $98 to $79. What is the amount of markdown? 

Beginning amount = $ 98 

New amount = $ 79 

Decrease = new amount − beginning amount 

= $ 98 − $ 79 

= $ 19 

The coat was marked down $19. 

Changes are often expressed as a percent of change. The amount of change is a percent of 

the original or beginning amount. 

Find the amount of change (increase or decrease) from a percent of change 

1. Identify the original or beginning amount and the percent or rate of change. 

2. Multiply the decimal or fractional equivalent of the rate of change times the original or 

beginning amount. 

EXAMPLE 

Your company has announced that you will receive a 3.2% raise. If your 

current salary is $42,560, how much will your raise be? 

What You Know 

Current salary $42,560 

Rate of change 3.2% 

Solution Plan 

Amount 

of raise 

= percent of 

change 

× 

original 

amount 

What You Are Looking For 

Amount of raise 

Solution 

Amount of raise = percent of change × original amount 

= 32 .% × $ 42560 , 

= 0. 032 × $ 42, 

560 

= $, 1 361. 

92 

Multiply. 

Conclusion 

The raise will be $1,361.92. 


1. The price of a new Lexus is $53,444. The previous year’s 

model cost $51,989. What is the amount of increase? 

$1,455 increase 

3. Marilyn Bauer earns $62,870 and gets a 4.3% raise. How 

much is her raise? 

$2,703.41 

5. Zack weighed 230 pounds before experiencing a 12% 

weight loss. How many pounds did he lose? 

27.6 pounds 

2. In trading on the New York Stock Exchange, Bank of 

America fell to $73.57. The stock had sold for $81.99. 

What is the amount of decrease in the stock price per share? 

$8.42 

4. International Paper reported third-quarter earnings were down 

16% from $145 million. What was the amount of decrease? 

$23.2 million or $23,200,000 



2 

 

Find the new amount directly in a percent problem. 

Often in increase or decrease problems we are more interested in the new amount than the amount 

of change. We can find the new amount directly by adding or subtracting percents first. The original 

or beginning amount is always considered to be our base and is 100% of itself. 

How To 

Find the new amount directly in a percent problem 

1. Find the rate of the new amount. 

For increase: 100% rate of increase 

For decrease: 100% rate of decrease 

2. Find the new amount. 

P = RB 

New amount = rate of new amount × original amount 

EXAMPLE 

Medical assistants are to receive a 9% increase in wages per hour. If they 

were making $15.25 an hour, what is the new wage per hour to the 

nearest cent? 

Rate of new amount = 100% 

+ rate of increase 

= 100% + 9% 

= 109% 


= 109%($ 15. 25) 

= 1091525 . ( . ) 

= $ 16. 

6225 

= $ 16. 

62 

The new hourly wage is $16.62. 

Change % to its decimal 

equivalent. 

Multiply. 

New amount 

Nearest cent 

EXAMPLE 

A pair of jeans that cost $49.99 is advertised as 70% off. What is the sale 

price of the jeans? 


− rate of decrease 

= 100% − 70% 

= 30% 


= 30%($ 49. 99) 

= 

= 

= 

034999 .( . ) 

$ 14. 

997 

$ 15. 

00 

Change % to its 

decimal equivalent. 

Multiply. 

New amount 

Nearest cent 


1. Marilyn Bauer earns $62,870 and gets a 4.3% raise. How 

much is her new salary? 

100% 4.3% 104.3% 

$65,573.41 

3. Zack weighed 230 pounds before experiencing a 12% 

weight loss. How many pounds does he now weigh? 

100% 12% 88% 

202.4 pounds 

2. International Paper reported third-quarter earnings were 

down 16% from $145 million. Find the third-quarter 

earnings. 

100% 16% 84% 

$121.8 million, or $121,800,000 

4. Over the next ten years Stacy Bauer plans to increase her 

investment of $9,500 by 250%. How much will she have 

invested altogether? 

100% 250% 350% 

$33,250 



5. Shares of McDonald’s, the world’s largest hamburger 

restaurant chain, rose 51% this year. Find the new share 

price if the stock sold for $24.25 last year. 

100% 51% 151% 

$36.62 

3 

 

Find the rate or the base in increase or decrease problems. 

Many kinds of increase or decrease problems involve finding either the rate or the base. 

The rate is the percent of change or the percent of increase or decrease. The base is still the 

original amount. 

How To 

Find the rate or the base in increase or decrease problems 

1. Identify or find the amount of increase or decrease. 

P 

2. To find the rate of increase or decrease, use the percentage formula R = . 

B 

amount of change 

R = 

original amount 

P 

3. To find the base or original amount, use the percentage formula B = . 

R 


B = 

rate of change 

EXAMPLE 

During the month of May, a graphic artist made a profit of $1,525. In June 

she made a profit of $1,708. What is the percent of increase in profit? 

What You Know 

Original amount 

New amount 

Solution Plan 

= 

= 

$, 1 525 

$, 1 708 

Amount of increase = new amount − original amount 

amount of increase 

Percent of increase = 



Percent of increase 

Solution 

Amount of increase = $, 1 708 − $, 1 525 

= $ 183 

$ 183 


$, 1 525 

= 012 . × 100% 

= 12% 

Conclusion 

The percent of increase in profit is 12%. 

Subtract. 

Divide. 

Convert to % equivalent. 

In some cases you may not have enough information to determine the amount of increase or 

decrease. Then we must match the rate with the information we are given. 

EXAMPLE 

At Best Buy the price of a DVD player dropped by 20% to $179. What 

was the original price to the nearest dollar? 



What You Know 

Reduced price = new amount = $ 179 

Rate of decrease = 20% 


Original price 

Solution Plan 

Not enough information given to find the amount of decrease. 

Rate of reduced price = 100% − rate of decrease 

Solution 

B= P R 

reduced price 

Original price = 

rate of reduced price 

Rate of reduced price = 100% − 20% 

= 80% 

$ 179 


80% 

179 

= 

08 . 

= $ 223. 

75 

= $ 224 

Convert % to decimal equivalent 

Divide. 

Round to nearest dollar. 

Conclusion 

The original price of the DVD player was $224. 

Ti p 

Be Sure to Use the Correct Rate 

When using the percentage formula, the description for the rate must match the portion. 

Look at the preceding example and the example on p. 186 

DVD Problem Jeans Problem 

Form of percentage formula B = 

P 

R 

P RB 

Description of rate Rate of reduced price Rate of new amount 

Description of portion Reduced price New amount 


1. Johanna Helba reported sales of $23,583,000 for the third 

quarter and $38,792,000 for the fourth quarter. What is the 

percent of increase in profit? Round to the nearest tenth of a 

percent. 

64.5% 

3. Maura Helba showed a house that was advertised as a 10% 

decrease on the original price. The sale price is $148,500. 

What was the original price? 

$165,000 

2. Stephen Helba reduced his college spending from $9,524 in 

the fall semester to $8,756 in the spring semester. What 

percent was the decrease? Round to the nearest percent. 

8% 

4. You know that a DVD is reduced 25% and the amount of 

reduction is $6.25. Find the original price and the 

discounted price of the movie. 

Original price: $25 

Discounted price: $18.75 

5. A used truck is reduced 48% of its new price. You know the 

used price is $14,799. Find the new price to the nearest 

dollar. 

$28,460 



News That Counts 

Recognition for Corporate 

Conscience 

Customers and employees want to do 

business with and work for companies 

they believe are helping to make the 

world a better place. Corporate philanthropy 

is growing in popularity as a cost 

effective means for building desirable 

corporate images. 

Based on the results of The Chronicle 

of Philanthropy’s annual survey of sales 

and cash donations for 2002, Wal-Mart 

Stores, Inc., was recognized as the 

“Largest Corporate Cash Giver.” This 

year’s survey of the 400 largest charities 

in the nation showed that donations 

dropped to $46.9 billion in 2002. This 

was down from $47.5 billion in 2001. 

While overall donations were down, Wal- 

Mart’s cash contributions increased in 

2002 to $136 million, up 17% from 2001. 

Wal-Mart’s contributions were 

shared with over 80,000 organizations in 

2002. Civic and community organizations 

received $53,699,000; community 

health and welfare, $43,488,000; education, 

$34,418,000, environmental concerns, 

$1,622,000, and other categories, 

$2,773,000. 

Wal-Mart Stores, Inc., was recognized 

for its corporate conscience. Even 

more important is the fact that the buying 

public will more than likely view the 

company favorably. 

Sources: The Chronicle of Philanthropy, 

October 30, 2003. 

www.walmartstores.com, “Wal-Mart Named America’s 

Largest Corporate Cash Giver,” October 29, 

2003, press release. 

Questions 

1. What is the percent of decrease in 

overall contributions to the 400 

charities during 2002 as compared 

to 2001? (Round to the nearest tenth 

of a percent.) 

2. Given the total dollar contribution for 

2002 and the percent of increase, 

what total dollar amount did Wal- 

Mart contribute during 2001? (Round 

to the nearest thousand dollars.) 

3. What percent of Wal-Mart’s contributions 

was made to each of the following 

categories? (Round to the 

nearest whole percent.) 

a) Civic and community 

b) Community health and welfare 

c) Education 

d) Environmental concerns 

Answers in IRM 



1. A number increased from 5,286 to 7,595. Find the amount 

of increase. 

7,595 5,286 2,309 

3. Find the amount of increase if 432 is increased by 25%. 

P = RB 

P = 025 . ( 432) 

P = 108 

5. If 135 is decreased by 75%, what is the new amount? 

Rate of new amount 100% 75% 25% 

P RB 

New amount 0.25(135) 33.75 

7. A number increased from 224 to 336. Find the percent of 

increase. 

Amount of increase = 336 − 224 

= 112 

P 

R = 

B 

amount of increase 

Rate of increase = 


112 

R = 

224 

R = 05 . × 100% 

R = 50% 

2. A number decreased from 486 to 104. Find the amount of 

decrease. 

486 104 382 

4. Find the amount of decrease if 68 is decreased by 15%. 

P = RB 

P = 01568 . ( ) 

P = 10. 

2 

6. If 78 is increased by 40%, what is the new amount? 

Rate of new amount 100% 40% 140% 

P RB 

New amount = 1.4(78) 

New amount = 109.2 

8. A number decreased from 250 to 195. Find the rate of decrease. 

Amount of decrease = 250 −195 

= 55 

P 

R = 

B 

amount of decrease 

Rate of decrease = 


55 

R = 

250 

R = 0. 

22 × 100% 

R = 22% 



9. A number is decreased by 40% to 525. What is the original 

amount? 

Rate represented 

= 100% −40% 

by new amount 

= 60% 

new amount 

Original number = 

rate represented by new amount 

525 


06 . 

Original number = 875 

10. A number is increased by 15% to 43.7. Find the original 

amount. 

Rate represented by new amount 100% 15% 115% 

new amount 


rate represented by new amount 

Original number = 43 . 7 

115 . 

Original number = 38 

Applications 

11. The cost of a pound of nails increased from $2.36 to $2.53. 

What is the percent of increase to the nearest wholenumber 

percent? 

Amount of increase = $. 253− $. 236 = $. 017 

P 

R = 

B 

017 . 

R = = 0. 

072 × 100% 

236 . 

R = 7% 

12. Wrigley recently announced an increase in the price of a 

five-stick pack of gum. This first increase in 16 years will 

raise the price by 5 cents to 30 cents. Find the percent of 

increase. Round to the nearest percent. 

Original price = 30 − 5 = 25 

P 

R = 

B 

5 

R = = 20% 

25 

13. Bret Davis is getting a 4.5% raise. His current salary is 

$38,950. How much will his raise be? 

P = RB 

P = 0. 045($38,950) 

P = $, 1 752. 

75 

14. Kewanna Johns plans to lose 12% of her weight in the next 

12 weeks. She currently weighs 218 pounds. How much 

does she expect to lose? 

P 

P 

P 

= 

= 

= 

RB 

012 . ( 218) 

26. 

16 pounds 

15. DeMarco Jones makes $13.95 per hour but is getting a 5.5% 

increase. What is his new wage per hour to the nearest cent? 



= 100% + 5. 5% 

= 105.% 

5 

rate of new original 

New amount = 

amount 

× 

amount 

= 105. 5%($ 13. 95) 

= 1. 055( 13. 95) 

= $ 14. 

71725 

= $ 14. 

72 

16. Carol Wynne bought a silver tray that originally cost $195 

and was advertised at 65% off. What was the sale price of 

the tray? 



= 100% − 65% 

= 35% 

rate of new original 

New amount = × 

amount amount 

= 35%( 195) 

= 035195 . ( ) 

= $ 68. 

25 

17. A laptop computer originally priced at $2,400 now sells for 

$2,700. What is the percent of increase? 

Amount of increase = new amount − original amount 

Amount of increase = 2, 700 − 2, 

400 

= $ 300 

$ 300 


$ 2, 

400 

= 0. 

125 × 100% 

= 12.% 

5 

18. Federated Department Stores dropped the price of a winter 

coat by 15% to $149. What was the original price to the 

nearest cent? 

Rate of reduced price = 100% − 15% = 85% 

reduced price 



$ 149 


85% 

$ 149 

= 

085 . 

= $ 175. 

29 



Chapter 6 

Summary 


Section 6-1 

1 Write 

2 Write 

Section 6-2 

1 Identify 

2 Use 

a whole number, 

fraction, or decimal as a 

percent. (p. 174) 

a percent as a whole 

number, fraction, or 

decimal. (p. 176) 

the rate, base, and 

portion in percent problems. 

(p. 178) 

the percentage formula 

to find the unknown value 

when two values are 

known. (p. 179) 

What to Remember with Examples 

1. Multiply the number by 1 in the form of 100%. 

2. The product has a % symbol. 

20 

3 3 100 

6 = 6 × 100% = 600% = × 

5 5 1 % = 60% 

0.075 = 0.075 × 100% = 7.5% 1 

1 

1. Divide by 1 in the form of 100% or multiply by . 

2. The quotient does not have a % symbol. 

100% 

48% = 48% ÷ 100% = 0.48 20% = 20% ÷ 100% = 20 = 

100 

157% = 157% ÷ 100% = 1.57 33 1 3 % = 331 3 % ÷ 100% = 0.33 1 3 

1. Rate is usually written as a percent, but may be a decimal or fraction. 

2. Base is the total or original amount. 

3. Portion is the part, or amount of increase or decrease. It is also called the percentage. 


42% of 18 is what number? 

42% is the rate. 

18 is the base. 

The missing number is the portion. 

1. Identify and classify the two known values and the one missing value. 

2. Choose the appropriate percentage formula for finding the missing value. 

3. Substitute the known values into the formula. For the rate, use the decimal or fractional 

equivalent of the percent. 

4. Perform the calculation indicated by the formula. 

5. Interpret the result. If finding the rate, convert decimal or fractional equivalents of the rate to 

a percent. 

1 

5 

1 

5 

or 0.33 

Find P if B 20 and R 15%. Find B if P 36 and R 9% 

P = R × B 

P = 15% ( 20) = 0. 15( 

20) 

P = 3 

P 

B = 

R 

36 

B = = 

9% 

B = 400 

36 

0.09 



Section 6-3 

1 Find the amount of increase 

or decrease in percent 

problems. (p. 184) 

2 Find 

3 Find 

the new amount 

directly in percent 


the rate or the base in 

increase or decrease 


1. To find the amount of increase: 

Amount of increase new amount beginning amount 

2. To find the amount of decrease: 

Amount of decrease beginning amount new amount. 

A truck odometer increased from 37,580.3 to 42,719.6. What was the increase? 

42,719.6 37,580.3 5,139.3 

A truck carrying 62,980 pounds of food delivered 36,520 pounds. What was the amount of 

food (pounds) remaining on the truck? 

62,980 36,520 26,460 pounds 

1. Find the rate of the new amount. 

For increase: 100% rate of increase 

For decrease: 100% rate of decrease 

2. Find the new amount. 

P RB 

New amount rate of new amount original amount 

Emily Denly works 30 hours a week but plans to increase her work hours by 20%. How 

many hours will she be working after the increase? 

For increase: 100% 20% 120% 

P 

P 

= 

= 

= 

= 

RB 

120%( 30 hours) 

120 . ( 30) 

36 hours 

1. Identify or find the amount of increase or decrease. 

P 

2. To find the rate of increase or decrease, use the percentage formula R = . 

B 


R = 


P 

3. To find the base or original amount, use the percentage formula B = . 

R 


B = 

rate of change 

Tancia Brown made a profit of $5,896 in June and a profit of $6,265 in July. What is the 

percent of increase? Round to tenths of a percent. 

Amount of increase = $ 6, 265 − $ 5, 896 = $ 369 


R = 


$ 369 

= 

$, 5 896 

= 0. 06258 × 100% 

= 63 .% 



NAME 

DATE 


Exercises Set A 


1. 0.23 

0.23 100% 0.23.; 23% 

4. 0.34 

0.34 100% 0.34.; 34% 

7. 3 

3 100% 3.00.; 300% 

10. 4 

4 4 100% 400% 

2. 0.82 

0.82 100% 0.82.; 82% 

5. 0.601 

0.601 100% 0.60.1; 60.1% 

8. 0.37 

0.37 0.37 100% 37% 

3. 0.03 

0.03 100% 0.03.; 3% 

6. 1 

1 100% 1.00.; 100% 

9. 0.2 

0.2 0.2 100% 20% 

Write the fraction or mixed number as a percent. Round to the nearest hundredth of a percent if necessary. 

11. 

17 

100 

17 

100 

= 17 

100 17 

100 × % = % 

12. 

6 

100 

6 

100 

6 

= × 100% = 6% 

100 

13. 

52 

100 

52 

100 

52 

= × 100% = 52% 

100 

14. 

1 

10 

1 

10 

1 

= × 100% = 10% 

10 

15. 

5 

4 

5 

4 

5 

= × 100% = 125% 

4 


16. 98% 

98% .98.% 100% 0.98 

17. 256% 

256% 2.56.% 100% 2.56 

18. 91.7% 

91.7% .91.7% 100% 0.917 

19. 0.5% 

0.5% .005% 100% 0.005 

20. 6% 

6% .06% 100% 0.06 

Write the percent as a whole number, mixed number, or fraction, reduced to lowest terms. 

21. 10% 

22. 6% 

23. 89% 

24. 45% 

25. 225% 

10% 

10 1 

100% = 100 

= 6% 

6 3 89% 

89 

10 100% = 100 

= 50 100% = 

45% 

45 9 

100 100% = 100 

= 225% 

225 

20 100% = 100 

= 

= 2 1 4 

2 25 

100 

Percent Fraction Decimal 

26. 33 1 1 

_______ _______ 

33 % 

033 1 33 1 100 1 1 

. or 0.33 % ÷ 100% = × = 33 1 % = 33 1 % ÷ 100% = 0. 

33 1 3 

3 

3 

3 100 3 3 3 

3 

1 

1 

125 1 

27. 12.5% _______ _______ 8 0.125 0. 125 × 100% = 12. 5% 0. 

125 = = 

4 

1, 

000 8 

28. 80% _______ _______ 5 

8 4 

0.8 08 . × 100% = 80% 

= 

10 5 

7 

29. 70% _______ _______ 07 . 07 . × 100% = 70% 10) 

7. . 

0 7 

10 

193


Find P, R, or B using the percentage formula or one of its forms. 

30. B = 300, R = 27% 

31. P = 25, 

B = 100 

P = RB 

P 

R = 

P = 027300 . ( ) 

B 

P = 81 

25 

R = 

100 

R = 025 . × 100% 

R = 25% 

32. P = $ 600, R = 5% 

P 

B = 

R 

$ 600 

B = 

005 . 

B = $ 12, 

000 

Round decimals to the nearest hundredth and percents to the nearest whole number percent. 

33. B = 36, R = 42% 

34. P = $ 835, R = 3. 2% 

35. P = 125, 

B = 50 

P = RB 

P 

P 

B = 

R = 

P = 042 . ( 36) 

R 

B 

P = 15. 

12 

$ 835 

125 

B = 

R = 

0. 

032 

50 

B = $ 26, 093. 

75 

R = 25 . × 100% 

R = 250% 

Use the percentage formula or one of its forms. 

36. Find 30% of 80. 

37. 90% 

of what number is 27? 

38. 51. 

52 is what percent of 2, 576? 

P RB 

P 

P 

P 0.3(80) 

B = 

R = 

R 

B 

P 24 

27 

51. 

52 

B = 

R = = 002 . × 100% 

09 . 

2, 

576 

B = 30 

R = 2% 

39. Jaime McMahan received a 7% pay increase. If he was 

earning $2,418 per month, what was the amount of the pay 

increase? 

P RB 

0.07(2,418) 

$169.26 

41. Seventy percent of a town’s population voted in an election. 

If 1,589 people voted, what is the population of the town? 

P 

B = 

R 

1, 

589 

B = 

07 . 

B = 2, 270 people 

43. The financial officer allows $3,400 for supplies in the 

annual budget. After three months, $898.32 has been spent 

on supplies. Is this figure within 25% of the annual budget? 

P 

R = 

B 

$ 898. 

32 

R = 

$, 3 400 

R = 0. 264211764 × 100% 

R = 26% 

26 % (rounded) is not within the budgeted 25% 

40. Eighty percent of one store’s customers paid with credit 

cards. Forty customers came in that day. How many 

customers paid for their purchases with credit cards? 

P RB 

0.8(40) 

32 customers 

42. Thirty-seven of 50 shareholders attended a meeting. What 

percent of the shareholders attended the meeting? 

P 

R = 

B 

37 

R = 

50 

R = 074 . × 100% 

R = 74% of the shareholders 

44. Chloe Denly’s rent of $940 per month was increased by 

8%. What is her new monthly rent? 



= 100% + 8% 

= 108% 


= 108%($ 940) 

= 108940 . ( ) 

= $, 1 015. 

20 

45. The price of a wireless phone increased by 14% to $165. 

What was the original price to the nearest dollar? 

Rate of new amount = 100% + 14% 

= 114% 

$ 165 


114% 

$ 165 

= 

114 . 

= $ 144. 

7368421 

= $ 145 

194


NAME 

DATE 


Exercises Set B 


1. 0.675 

0.675 100% 0.67.5; 67.5% 

2. 2.63 

2.63 100% 2.63.; 263% 

3. 0.007 

0.007 100% 0.00.7; 0.7% 

4. 3.741 

3.741 100% 3.74.1; 374.1% 

5. 0.0004 

0.0004 100% 0.00.04; 0.04% 

6. 0.6 

0.6 100% 0.60.; 60% 

7. 0.242 

0.242 100% 0.24.2; 24.2% 

10. 0.03 

0.03 100% 0.03.; 3% 

8. 0.811 

0.811 100% 0.81.1; 81.1% 

9. 2.54 

2.54 100% 2.54.; 254% 

Write the fraction or mixed number as a percent. Round to the nearest hundredth of a percent if necessary. 

11. 

99 

100 

99 100 % 

× = 99% 

100 1 

1 

1 

12. 

20 

100 

20 100 % 

× = 20% 

100 1 

1 

1 

13. 

13 

20 

13 100 % 

× = 65% 

20 1 

1 

5 

14. 

3 2 5 

3 2 17 100 % 

× 100% 

= × = 340% 

5 

5 1 

1 

20 

15. 

2 

5 

2 100 % 

× = 

5 1 

1 

20 

40% 


16. 84.6% 

84.6% 100% 0.846 

17. 52% 

52% 100% 0.52 

18. 3% 

3% 100% 0.03 

19. 0.02% 

0.02% 100% 0.0002 

20. 274% 

274% 100% 2.74 

Write the percent as a whole number, mixed number, or fraction, reduced to lowest terms. 

21. 20% 

22. 170% 

20 

20% ÷ 100% 

= = 

100 

1 

5 

170 17 

170% ÷ 100% 

= = = 

100 10 

1 7 

10 

23. 361% 

361 

361% ÷ 100% 

= = 

100 

3 61 

100 

24. 25% 

25 

25% ÷ 100% 

= = 

100 

1 

4 

25. 

12 1 2 % 

12 1 12 1 1 

100 2 25 100 25 1 

% ÷ % = = ÷ = × = 

2 

100 2 1 2 100 

4 

1 

8 

195


Percent Fraction 

2 

Decimal 

27. 50% _______ 2 _______ 0.5 

28. 87 1 7 

_______ _______ 

2 % 8 0.875 

9 

26. _______ 40% 5 

1 

_______ 0.4 

29. _______ 45% _______ 20 0.45 

26. 2 100% 

27. 

× = 40% 

5 1 

1 

04 

520 . . 

) 

20 

50 

50% ÷ 100% 

= = 

100 

50% ÷ 100% = 0. 

5 

7 

28. 87 1 100 87 1 175 1 7 

% ÷ % = ÷ 100 = × = 29. 045 . × 100% = 45% 

2 

2 2 100 8 

45 9 

045 . = = 

100 20 

87 1 4 

% = 87. 5% ÷ 100% = 0. 

875 

2 

1 

2 

Find P, R, or B using the percentage formula or one of its forms. 

30. B $1,900, R 106% 

P = RB 

P = $, 1 900( 106%) 

P = $, 1 900(. 1 06) 

P = $ 2, 

014 

31. P 170, B 85 

P 

R = 

B 

170 

R = 

85 

R = 2 

R = 200% 

32. P $15.50, R 7.75% 

P 

B = 

R 

$ 15. 

50 

B = 

775 . % 

$ 15. 

50 

B = 

. 0775 

B = $ 200 

Round decimals to the nearest hundredth and percents to the nearest whole number percent. 

33. P 68, B 85 

P 

R = 

B 

68 

R = 

85 

R = 08 . 

R = 80% 

34. R 72%, B 16 

P = RB 

P = 72%( 16) 

P = 07216 . ( ) 

P = 11. 

52 

35. P 52, R 17% 

P 

B = 

R 

52 

B = 

17% 

52 

B = 

017 . 

B = 305. 

88 


36. Find 150% of 20. 

P RB; P 1.5(20); P 30 


P 27 

R = ; R = ; R = 3 × 100%; R = 300% 

B 9 

40. If a picture frame costs $30 and the tax on the frame is 6% 

of the cost, how much is the tax on the picture frame? 

$30(0.06) $1.80 tax 

42. The United Way expects to raise $63 million in its current 

drive. The chairperson projects that 60% of the funds will 

be raised in the first 12 weeks. How many dollars are 

expected to be raised in the first 12 weeks? 

$63,000,000(0.6) $37,800,000 

44. Last year Docie Johnson had net sales of $582,496. This 

year her sales decreased by 12%. What were her net sales 

this year? 

Rate of this year’ s sales = 100% −12% 

= 88% or 0.88 

Rate of this 

This year sales amount = 

year sales 

× last year sales 

This year sales amount = 088582 . ( , 496) 

= $ 512, 596. 

48 

196 

37. 82% of what number is 94.3? 

P 

B = R ; B = 94. 

3 

; 

082 . 

B =115 

39. Ernestine Monahan draws $1,800 monthly retirement. On 

January 1, she received a 3% cost of living increase. How 

much was the increase? 

$1,800(0.03) $54 

41. Five percent of a batch of fuses were found to be faulty 

during an inspection. If 27 fuses were faulty, how many 

fuses were inspected? 

27 

= 540 fuses 

005 . 

43. An accountant who is currently earning $42,380 annually 

expects a 6.5% raise. What is the amount of the expected 

raise? 

$42,380(0.065) $2,754.70 

45. The price of Internet service decreased by 7% to $52. What 

was the original price to the nearest dollar? 

Rate of reduced price = 100% − 7% 

= 93% or 0.93 

52 


093 . 

= $ 55. 

9139 

= $ 56



Practice Test 


1. 0.24 

0.24. 100% 24% 

2. 0.925 

0.92.5 100% 92.5% 

3. 0.6 

0.60. 100% 60% 

Write the fraction or mixed number as a percent. 

4. 

21 

100 

21 

× 100% = 21% 

100 

5. 

3 

8 6. Write 

1 % 4 

as a fraction. 

25 

3 100% 75% 

1 

1 1 

% ÷ 100% 

= × = 

× = = 37.% 

5 

4 

4 100 

8 1 2 

2 

1 

400 


7. Find 30% of $240. 

P R B 0.3 $240 $72 


P 

R = B 

= 50 

= 25 . 

20 

= 25 . × 100% = 250% 


P 

R = B 

= 7 

= 0.875 

8 

= 87.5%, or 87 1 2 % 

10. What is the sales tax on an item that costs $42 if the tax rate is 6%? 

P RB 0.06(42) $2.52 

12. Twelve employees at a meat packing plant were sick on Monday. 

If the plant employs 360 people, what percent to the nearest whole 

percent of the employees was sick on Monday? 

P 

R = B 

= 12 

= 0. 03333 

360 

= 3% 

11. If 100% of 22 rooms are full, how many rooms are full? 

P RB 100%(22) 1(22) 22 

13. A department store had 15% turnover in personnel last year. If the 

store employs 600 people, how many employees were replaced 

last year? 

P RB 15%(600) 0.15(600) 90 employees 

14. The Dawson family left a 15% tip for a restaurant check. If the 

check totaled $19.47, find the amount of the tip. What was the 

total cost of the meal, including the tip? 

P RB 15%($19.47) 0.15($19.47) $2.92 tip 

Total bill $19.47 $2.92 $22.39 

16. Of the 20 questions on this practice test, 11 are word problems. 

What percent of the problems are word problems? (Round to the 

nearest whole number percent.) 

P 

R = B 

= 11 

= 055 . 

20 

= 55% 

18. Byron Johnson took a pay cut of 5%. He was earning $148,200 

annually. What is his new annual salary? 



= 100% − 5% 

= 95% 

rate of new 

New amount = 

amount 

× original amount 

= 95%($ 148, 200) 

= 095148 . ( , 200) 

= $ 140, 

790 

15. A certain make and model of automobile was projected to have a 

3% rate of defective autos. If the number of defective automobiles 

was projected to be 1,698, how many automobiles were to be 

produced? 

P 

B = R 

= 1, 

698 

3 

= 1, 

698 

% 003 . 

= 56, 

600 automobiles 

17. Frances Johnson received a 6.2% increase in earnings. She was 

earning $86,900 annually. What is her new annual earnings? 



= 100% + 6. 2% 

= 106.% 

2 

rate of new 

New amount = 

amount 

× original amount 

= 106. 2%($ 86, 900) 

= 1. 062( 86, 900) 

= $ 92, 287. 

80 

19. Sylvia Williams bought a microwave oven that had been reduced 

by 30% to $340. What was the original price of the oven? Round 

to the nearest dollar. 

Rate of reduced price = 100% 


= 100% − 30% 

= 70% 

reduced price 



$ 340 

= 

70% 

$ 340 

= 

07 . 

= $ 485. 

7142 

= $ 486 

197


20. Sony decided to increase the wholesale price of its DVD players 

by 18% to $320. What was the original price rounded to the 

nearest cent? 

Rate of increased price = 100% + 18% 

= 118% 


= 

= 

= 

= 

increased price 

rate of increased price 

$320 

118% 

$320 

1.18 

$271.1864 

$271.19 


Critical Thinking 

1 

1. Numbers between 100 and 1 are equivalent to percents that are 2. Percents between 0% and 1% are equivalent to fractions or 

between 1% and 100%. Numbers greater than 1 are equivalent to 

decimals in what interval? 

1 

percents that are ____. 

Fractions greater than 0 and less than 100 ; decimals greater than 0 

More than 100% 

and less than 0.01 

3. Explain why any number can be multiplied by 100% without 

changing the value of the number. 

Multiplying by 100% is equivalent to multiplying by 1 and any 

number multiplied by 1 results in the same number. 

4. Can any number be divided by 100% without changing the value 

of the number? Explain. 

Yes, dividing by 100% is the same as dividing by 1 and dividing 

by 1 does not change the value of the number. 

5. A conjugate of a percent is the difference of 100% and the given 

percent. What is the conjugate percent of 48%? 

100% 48% 52% 

6. Which one of the three elements of the percentage formula 

requires multiplication? 

Finding the portion or percentage requires multiplying the base 

times the rate. 

7. If the cost of an item increases by 100%, what is the effect of the 

increase on the original amount? Give an example to illustrate 

your point. 

A 100% increase doubles the original amount. I have $30 and 

increase it by 100%. 

Percent of new amount = 100% 

+ percent of increase 

= 100% + 100% 

= 200% 

New amount = RB 

= 200%(30) 

= 230 ( ) 

= $ 60 

Challenge Problem 

Brian Sangean has been offered a job in which he will be paid strictly on a commission basis. He expects to receive a 4% commission on all sales of 

computer hardware he closes. Brian’s goal for a gross yearly salary is $36,000. How much computer hardware must Brian sell in order to meet his target 

salary? 

P 

B = 

R 

$ 60, 

000 

B = 

4% 

$ 60, 

000 

B = 

004 . 

B = $, 1 500, 

000 sales 

198


Case Study 

NAME 

DATE 

WASTING MONEY OR SHAPING UP? 

Sarah belongs to a gym and health spa that is conveniently located between her 

home and her job. It is one of the nicer gyms in town, and Sarah pays $90 a 

month for membership. Sarah works out three times a week regularly. While she 

was getting off the treadmill one day, one of the club’s personal trainers came 

by to talk and offered to plan a routine for Sarah that would help her train for an 

upcoming marathon. The trainer had noticed that Sarah came in regularly, and 

she commented that most members don’t have the self-control to do that. In fact, 

she explained that there is a study of 8,000 members in Boston area gyms that 

showed that members went to the gym only about five times per month. The 

study also found that people who choose a pay-per-visit membership spend less 

money then people who choose a monthly or annual membership fee. 

1. At Sarah’s club the pay-per-visit fee is $5 per day. Would Sarah save 

money paying-per-visit? Assume that a month has 4.3 weeks. What percentage 

of her monthly $90 fee would she spend if she paid on a per-visit basis? 

3 visits per week 4.3 weeks in a month 13 visits per month 

$90 

13 

$6.92 per visit 

Yes, Sarah would save money if she paid $5 per visit. 

$5 13 visits $65 spent per month if pay-per-visit 

65 

90 .7222 72% 

2. If Sarah goes to the gym three times per week, what portion of the year does she use the gym? 

3 times 52 weeks 156 visits per year 

days in a year 0.427 43% of the days in a year 

156 

365 

3. If Sarah went to the gym every day, how much would she pay per day on the monthly payment plan? Assume 30 days in a month. 

If she went every day and paid $5 per day, how much would she be spending per month? How much more is this in percentage 

terms compared to the $90 monthly rate rounded to the nearest percent? 

90 

30 

$3 per day if she goes daily on monthly plan 

$5 30 $150 per month on per-visit plan 

$150 90 $60 difference in plans 

100% 67% percent that the per-visit plan is more than the monthly plan 

60 

90 

Source: “Why You Waste So Much Money,” Wall Street Journal, Wednesday, July 14, 2003, p. D1. 



Case Study 

NAME 

DATE 

BATTLING SOUPS 

Managers in the marketing department at Campbell’s Soup have recent market 

research that shows that the company is losing market share of the readyto-serve 

soup market to General Mills Progresso soup. In 1998, Campbell held 

a 74.5% market share versus Progresso’s 9.2%. By 2002 Campbell’s market 

share had decreased to 68.6%, while Progresso’s increased to 13.5%. Total industry 

sales for ready-to-serve soups in 2002 were $1.78 billion, up from 

$1.27 billion in 1998. Curiously, as the ready-to-serve market has grown, the 

condensed soup market has declined from $1.55 billion sales in 1998 to $1.33 

billion sales in 2002. In 2002, Campbell’s had 84% of the condensed soup 

market. The marketing managers have been studying the market share situation 

for clues that may determine future strategy decisions at Campbell’s. 

1. How much did Campbell’s and Progresso’s market shares change between 

1998 and 2002? 

Campbell’s (68.6% 74.5% 5.9%) ↓ 5.9% from 1998 to 2002 

Progresso (13.5% 9.2% 4.3%) ↑ 4.3% from 1998 to 2002 

2. How much market shares did other companies have in 1998 and in 2002? 

2002 1998 

Campbell’ s 68. 6% 74.% 

5 

Progresso + 13.% 5 + 9.% 

2 

82.% 1 83.% 

7 

100% − 82. 1% = 17. 9% 100% − 83.% 7 = 16.% 

3 

3. Make a table to represent the percent of shares for Campbell’s, Progresso, the others, and the total industry market shares in 2002 

and in 1998. 

2002 1998 

Campbell’s 68.6% 74.5% 

Progresso 13.5% 9.2% 

Others 17.9% 16.3% 

Total market 100% 100% 

4. What was Campbell’s total sales revenue for ready-to-serve soup and condensed soup in 2002? Round to the nearest tenth of a 

billion. 

Ready-to-serve soup 

2002 $. 178 billion × 0686 . = 1. 22108 = 1. 

2 billion 

Condensed soup 

2002 $1.33 billion × 084 . = 1. 1172 = 1. 

1 billion 

$1.2 billion + $. 11billion = $2.3 billion 

Source: “Campbell’s Comeback Strategy: Reheating Condensed Soup,” Wall Street Journal, July 31, 2003, p. A1. 

200


The Real World! Video Case 

HOW MANY HAMBURGERS? 

Business Math Topics Covered 

1. Basic Equations 

2. Decimals 

Learning Objectives 

After viewing this video, you should be able to: 

1. Calculate and compare order quantities based upon historical 

information. 

2. Identify a variety of business variables involved in making 

purchasing decisions. 

Synopsis 

While Charlie is out of the shop, a local meat vendor calls and 

asks to speak to the manager of Brubaker’s Grill regarding an attractive 

deal he can offer on hamburger meat. Joe is excited to talk 

with the vendor. He is anxious to prove to Charlie that he can be 

a manager, so he sits down with the vendor to explore the offer. 

The deal, as proposed by the vendor, would require Brubaker’s to 

buy a lot of hamburgers, but the price per patty sounds very attractive. 

Joe listens to the proposal and wonders if this offer is 

worth pursuing, given their historical rate of hamburger usage and 

the prices per patty that they are currently paying. 

Worksheet and Video 

Discussion Questions 

1. Download the worksheet for this video and after viewing 

the video, utilize the worksheet to compare the new deal 

and the existing deal. What is positive about the new deal? 

What is negative about the new deal? 

2. What factors should Joe consider, beyond the price per 

patty, before making a recommendation to Charlie? 

201

Chapter 6: Percents

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