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Rates and Unit Pricing5.2

421

5.2 OBJECTIVES

1. Write a rate as a fraction2. Find unit rates3. Find unit prices

Example 1

Finding a Rate

Find each rate.

(a)

(b)

(c)10 gallons

200 miles�

10

200 gal

mi�

1

20 gal

mi

E F

200 miles

10 gallons�

200

10 mi

gal� 20

mi

gal

12 feet

16 seconds�

12

16 ft

s�

3

4 ft

s

A ratio compares two denominate numbers. Examples of a ratio include

or

In these examples, the units of the numerator and denominator are identical. When we com-pare denominate numbers with different units, we get a rate.

5 miles

7 miles�

5

7

9 seconds

12 seconds�

9

12�

3

4

C H E C K Y O U R S E L F 1

Find each rate.

(a) (b) (c)2 years

$60,000

$60,000

2 years

250 miles

10 hours

Sometimes, we need to find the appropriate rate within a statement, as in the next example.

422 CHAPTER 5 RATIOS AND PROPORTIONS

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Example 2

Finding a Rate

Randy Johnson had 320 strikeouts in 280 innings. What was his strikeout per inning rate?

� 11

7 strikeouts

inning

320 strikeouts

280 innings�

320

280 strikeouts

inning

C H E C K Y O U R S E L F 2

Chamique Holdsclaw scored 450 points in 15 games. What was her points/gamerate?

NOTE Recall that in Section 5.1we stated that mixed numberswere inappropriate for ratios.When we write a rate, a mixednumber is not just appropriate,it is preferred.

One purpose for computing a rate is for comparison. Example 3 illustrates.

Example 3

Comparing Rates

Player A scores 50 points in 9 games and player B scores 260 points in 36 games. Whichplayer scored at a higher rate?

Player A’s rate was

Player B’s rate was

Player B scored at a higher rate.

� 7.22 points

game

�65

9 points

game

260 points

36 games�

260

36 points

game

� 5.56 points

game

50 points

9 games�

50

9 points

game

C H E C K Y O U R S E L F 3

Hassan scored 25 goals in 8 games and Lee scored 52 goals in 18 games. Whichplayer scored at a higher rate?

RATES AND UNIT PRICING SECTION 5.2 423©

200

1 M

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ies

There is one rate that is posted on every item in most supermarkets.

The unit price (or unit rate) relates a price to some common unit.

Definitions: Unit Price

Example 4

Finding a Unit Price

Find the unit price for each item.

(a) 8 ounces of cream cost $1.53

(b) 20 pounds of potatoes cost $3.98

� 20 cents

lb

�398

20 cents

lb

$3.98

20 pounds�

398 cents

20 pounds

� 19 cents

oz

$1.53

8 ounces�

153 cents

8 ounces�

153

8 cents

oz

NOTE A unit price is a price perunit. The unit used may beounces, pints, pounds, or someother unit.

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C H E C K Y O U R S E L F 4

Find the unit price for each item.

(a) 12 soda cans cost $2.98 (b) 25 pounds of dog food cost $9.99

C H E C K Y O U R S E L F A N S W E R S

1. (a) 25 ; (b) 30,000 ; (c) 2. 30

3. Hassan had a higher rate 4. (a) � 25 ; (b) � 40 cents

lb

cents

can

points

game

1

30,000

yr

dollar

dollars

yr

mi

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Exercises

Find each rate.

1. 2.

3. 4.

5. 6.

7. 8.

9. 10.

11. 12.

13. 14.

15. 16.

Solve the following applications.

17. Trac drives 256 miles using 8 gallons of gasoline. How many miles per gallon doeshis car get?

18. Seven pounds of fertilizer cover fourteen hundred square feet. How many square feetare covered by one pound of fertilizer?

19. A local college has 6000 registered vehicles for 2400 campus parking spaces. Howmany vehicles are there for each parking space?

657,200 library books

5200 students

192 diapers

32 babies

240 pounds of fertilizer

6 lawns

150 calories

3 ounces

$2,000,000

4 years

57 ounces

3 cans

7200 revolutions

16 miles

15 gallons

480 miles

480 miles

15 gallons

680 feet

17 seconds

5 years

$10,000

$10,000

5 years

3 seconds

69 feet

69 feet

3 seconds

95 ¢

5 pencils

300 miles

4 hours

5.2

Name

Section Date

ANSWERS

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

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20. Curt Schilling has 141 strikeouts in 163 innings. What was his strikeout per inningrate?

21. A water pump can produce 280 gallons in 24 hours. How many gallons per hour isthis?

22. The sum of $5992 was spent for 214 shares of stock. What was the cost per share?

23. A printer produces 4 pages of print in 6 seconds. How many pages are produced persecond?

24. Augie eats 12 hamburgers in 48 minutes. How many minutes does it take Augie to eatone hamburger?

25. A 12-ounce can of tuna costs $4.80. What is the cost of tuna per ounce?

26. The fabric for a dress costs $76.45 for 9 yards. What is the cost per yard?

27. Gerry laid 634 bricks in 35 minutes and his friend Matt laid 515 bricks in 27 minutes.Who is the faster bricklayer?

28. Mike drove 135 miles in 2.5 hours. Sam drove 91 miles in 1.75 hours. Who drives atthe faster speed?

ANSWERS

20.

21.

22.

23.

24.

25.

26.

27.

28.

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39. Salad oil (1 qt is 32 oz):

(a) 18 oz for 89¢

(b) 1 qt for $1.39

(c) 1 qt 16 oz for $2.19

40. Tomato juice (1 pt is 16 oz):

(a) 8 oz for 37¢

(b) 1 pt 10 oz for $1.19

(c) 1 qt 14 oz for $1.99

41. Peanut butter (1 lb is 16 oz): 42. Laundry detergent:

(a) 12 oz for $1.25 (a) 1 lb 2 oz for $1.99

(b) 18 oz for $1.72 (b) 1 lb 12 oz for $2.89

(c) 1 lb 12 oz for $2.59 (c) 2 lb 8 oz for $4.19

(d) 2 lb 8 oz for $3.76 (d) 5 lb for $7.99

Answers

1. 75 3. 23 5. 2000 7. 9. �

11. 13. 15. 17.

19. 2.5 vehicles per space 21. � 23. 25. 40

27. Matt 29. Larry Walker 31. 33. 35. b

37. c 39. b 41. c

$0.43

orange

$11.50

shirt

centsounce

2

3 page11.67

gal

h

32 mi

gal6

diapers

baby50

cal

oz19

oz

can

0.03 gal

mi40

ft

s

dollars

year

ft

s

mi

h

ANSWERS

39.

40.

41.

42.

428