Chapter 3: Solving Equations

3.4Ratio & Proportion

Vocabulary

• Ratio:– Comparison of two numbers by division

• Rate:– If a and b represent quantities in different units, then

the ratio of a to b is a rate

• Unit Rate:– Rate with a denominator of 1

Example 1• The table gives prices for different sizes of the same

brand of apple juice. Find the unit rate (cost per ounce) for each. Which has the lowest cost per ounce?

Price Volume

$.72 16 oz

$1.20 32 oz

$1.60 64 oz

Example 1a• Main Street Florist sells two dozen roses for $24.60.

Flowers for You Florist sells six roses for $7.50. Find the unit rate for each. Which florist has the lower cost per rose?

Example 2• In 2004, Lance Armstrong won the Tour de France,

completing the 3391 km course in about 83.6 hours. Find Lance’s unit rate, which is his average speed. Write a rule to describe the distance he cycles d as a function of the time t he cycles. Cycling at his average speed, about how long would it take Lance to cycle 185 km?

Example 2a• Suppose you walk 2 miles in 35 minutes.• Find the average walking speed. Write a rule to

describe the distance d you walk as a function of the time t you walk.

• Use the function to find how far you would walk in an hour.

Example 3

• A cheetah ran 300 feet in 2.92 seconds. What was the cheetah’s average speed in miles per hour?

Example 3a

• A sloth travels 0.15 miles per hour. Convert this speed to feet per minute.

Proportions

• An equation that states that two ratios are equal

Example 4

• Solve:6

5

9t

Example 4a

• Solve:6

5

8x

Example 4b

• Solve:7

4

12

y

Example 4c

• Solve:1550

18 m

Cross Products of a Proportion

• If , then ad = bcd

c

b

a

Example 5• A box of cereal weighing 354 grams contains 20

grams of fat. Find the number of grams of fat in the recommended serving size of 55 grams.

Example 5a

• Solve:12

25

4x

Example 5b

• Solve:75

24 y

Example 5c

• Solve:64

7254

d

Example 6• Solve the proportion:

7

2

5

4

xx

Example 6a• Solve the proportion:

1014

2 xx

Example 6b• Solve the proportion:

7

35

4

15

y

y

Example 6c• Solve the proportion:

4

5

6

3

ww

Homework

• P. 145

• 6, 8, 14, 16 – 46 even