Chapter 9 - XYZ Custom Plus

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Chapter 9 Solving Equations and Inequalities
Step 3 Reread and write an equation. Because the total value of all the coins is
$1.60, the equation that describes this situation is
Amount of money
in nickels
5
Amount of money Total amount
1 5
in dimes of money
0.05x 1 0.10(x 1 7) 5 1.60
Step 4 Solve the equation. This time, let’s show only the essential steps in the
solution.
5
0.05x 1 0.10x 1 0.70 5 1.60 Distributive property
0.15x 1 0.70 5 1.60 Add 0.05x and 0.10x to get 0.15x
0.15x 5 0.90 Add −0.70 to each side
x 5 6 Divide each side by 0.15
Step 5 Write the answer. Because x 5 6, Diane has 6 nickels. To find the number
of dimes, we add 7 to the number of nickels (she has 7 more dimes than
nickels). The number of dimes is 6 1 7 5 13.
Step 6 Reread and check. Here is a check of our results.
5
6 nickels are worth 6($0.05) 5 $0.30
13 dimes are worth 13($0.10) 5 $1.30
The total value is $1.60
Getting Ready for Class
After reading through the preceding section, respond in your own
words and in complete sentences.
1. What is the first step in solving a word problem?
2. Write a mathematical expression equivalent to the phrase “the sum of x
and ten.”
3. Write a mathematical expression equivalent to the phrase “twice the
sum of a number and ten.”
4. Suppose the length of a rectangle is three times the width. If we let x
represent the width of the rectangle, what expression do we use to represent
the length?
Answer
7. There are 3 quarters and 10
dimes.