Basic Mathematics for College Students

5.1 Ratios 423

EXAMPLE (^10) Comparison Shopping
Olives come packaged in a 10-ounce jar, which
sells for $2.49, or in a 6-ounce jar, which sells for
$1.53. Which is the better buy?
StrategyWe will find the unit price for each jar
of olives. Then we will identify which jar has the
lower unit price.
WHYThe better buy is the jar of olives that has the lower unit price.
Solution
To find the unit price of each jar of olives, we write the quotient of its price and its
weight, and then perform the indicated division. Before dividing, we convert each
price from dollars to cents so that the unit price can be expressed in cents per
ounce.
The 10-ounce jar:
Write the rate:.
Then change $2.49 to 249 cents.
The 6-ounce jar:
Write the rate:.
Then change $1.53 to 153 cents.
Do the division.
One ounce for 24.9¢ is a better buy than one ounce for 25.5¢. The unit price is less
when olives are packaged in 10-ounce jars, so that is the better buy.
 25.5¢ per oz
price
$1.53 number of units
6 oz



153¢

6 oz

Divide 249 by 10 by moving the

 24.9¢ per oz decimal point 1 place to the left.

price

$2.49 number of units

10 oz



249¢

10 oz

$2.49 $1.53

NAPA’S BEST NAPA’S BEST

10 oz 6 oz

Self Check 10

COMPARISON SHOPPINGA

fast-food restaurant sells

a 12-ounce cola for 72¢ and a

16-ounce cola for 99¢. Which

is the better buy?

Now TryProblems 65 and 101

1. a. b. 2. 3. a. b. 4. 5. 6. 7.
   8.17 calories/oz 9.$10.90 per hour 10.the 12-oz cola

6 feet

7 days

2

3

3

1

1

3

3

2

2

3

4

3

8

15

4

9

ANSWERS TO SELF CHECKS

Fill in the blanks.

1. A is the quotient of two numbers or the
   quotient of two quantities that have the same units.


2. A is the quotient of two quantities that have
   different units.


3. A rate is a rate in which the denominator is 1.


4. A unit is a rate that tells how much is paid for
   one unit or one item.

VOCABULARY

5. To write the ratio in lowest terms, we remove any
   common factors of the numerator and denominator.
   What common factor do they have?


6. Complete the solution. Write the ratio in lowest
   terms.

14

21



2  7





2  7

1

 7

1



14

21

15

24

CONCEPTS

SECTION 5.1 STUDY SET

25.5

(^6) 153.0
 12
33
 30
30
 30
0