Fundamentals of Mathematics, 2008a

434 CHAPTER 7. RATIOS AND RATES
Example 7.20
The ratio of men to women in a particular town is 3 to 5. How many women are there in the town
if there are 19,200 men in town?
Step 1: The unknown quantity is the number of women in town.
Let x = number of women in town.
Step 2: The three specied numbers are
3
5
19,200
Step 3: The comparisons are 3 men to 5 women → 3 5
19,200 men to x women → 19,200
x
3
5 = 19,200
x
Step 4:
3
5
= 19,200
x
3 · x = 19, 200 · 5
3 · x = 96, 000
x =
96,000
3
x = 32, 000
Step 5: There are 32,000 women in town.
Example 7.21
The rate of wins to losses of a particular baseball team is 9 2
. How many games did this team lose
if they won 63 games?
Step 1: The unknown quantity is the number of games lost.
Let n = number of games lost.
Step 2: Since 9 2→ means 9 wins to 2 losses, the three specied numbers are
9 (wins)
2 (losses)
63 (wins)
Step 3: The comparisons are
9 wins to 2 losses→ 9 2
63 wins to n losses → 63 n
9
2 = 63 n
Step 4:
9
2
= 63
n
9 · n = 2 · 63
9 · n = 126
n = 126
9
n = 14
Step 5: This team had 14 losses.
Try Exercise 7.4.4 in Section 7.4.3.2 (Practice Set A).
7.4.3.2 Practice Set A
Solve each problem.
Exercise 7.4.1 (Solution on p. 468.)
On a map, 3 inches represents 100 miles. How many miles are represented by 15 inches?
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