Solving Proportions4-2

Bell work:Find two ratios that are equivalent to each given ratio.

35

1.

4530

3. 9060

32

,

1012

2. 2024

56

,

89

4. 2427

1618

,

915

610

,Possible answers:

Solving Proportions4-2

Problem of the DayWhat is the better buy?

A $1.29 pack of gum that has 15 pieces,OrA $1.59 pack of gum that has 20 pieces?

Explain your answer.

Solving Proportions4-2

Learning Target: I can tell if ratios are proportional.I can solve a proportion.

Solving Proportions4-2

Vocabulary

RatioRatio

ProportionProportion

Cross ProductCross Product

Solving Proportions4-2

Tell whether the ratios are proportional.

410

615

Since the cross products are equal, the ratios are proportional.

60

=?

60 = 60

Find cross products.60410

615

Solving Proportions4-2

Tell whether the ratios are proportional.

Since the cross products are equal, the ratios are proportional.

20

20 = 20

Find cross products.2024

510

24

510

=?

Solving Proportions4-2

A mixture of fuel for a certain small engine should be 4 parts gasoline to 1 part oil. If you combine 5 quarts of oil with 15 quarts of gasoline, will the mixture be correct?

4 parts gas1 part oil

=? 15 quarts gas5 quarts oil

4 • 5 = 20 1 • 15 = 15

20 ≠ 15

The cross products are not equal. The mixture will not be correct.

Set up equal ratios.

Find the cross products.

Solving Proportions4-2

A mixture for a certain brand of tea should be 3 parts tea to 1 part sugar. If you combine 4 tablespoons of sugar with 12 tablespoons of tea, will the mixture be correct?

3 parts tea 1 part sugar

=? 12 T tea4 T sugar

3 • 4 = 12 1 • 12 = 12

12 = 12

The cross products are equal. The mixture will be correct.

Set up equal ratios.

Find the cross products.

Solving Proportions4-2

The ratio of boys to girls in a soccer league is 5:4. If there are 55 boys in the league, how many girls are there?

54

boysgirls

=

54

=55x

x = 44

5x = 220

There are 44 girls in the league.

Solving Proportions4-2

The ratio of cats to dogs at a kennel is 3:2. If there are 48 dogs at the kennel, how many cats are there?

32

CatsDogs

=

32

= x48

x = 72

2x = 144

There are 72 cats at the kennel.

Solving Proportions4-2

A banana slug travels 4.5 inches in 120 minutes. At this rate of speed, how long would it take the slug to travel 12 inches?

4.5 in120 min

= 12 ins

One option is to use a proportion: inches/minute.

4.5s = 1440

s = 320 minutes

Solving Proportions4-2

A cable car travels 15 miles in 80 minutes. At this rate of speed, how long would it take the cable car to travel 45 miles?

x = 240

15 miles80 min

= 45 milesx

15x = 3600

Solving Proportions4-2

Lesson Quiz

Tell whether the ratios are proportional.

4842 =? 16

141. 40

15 =? 34

2.

Solve each proportion.

3. 4.

5. An elevator travels 342 feet as it goes from the lobby of a building to the top floor. It takes 7 seconds to travel the first 133 feet. If the elevator travels at the same rate, how much longer does it take reach the top floor?

yes no

n = 30 n = 16

11s

4518

n12 = n

2469 =

Solving Proportions4-2

Assignment:

Lesson 4.2, page 164, 9-16, 26-31