Lesson 3 MI/Vocab equivalent ratios proportion cross products constant of proportionality Use proportions to solve problems.

• equivalent ratios

• proportion

• cross products

• constant of proportionality

• Use proportions to solve problems.

Interactive Lab: Solving Problems

Write and Solve a Proportion

CLOTHING Melvin can decorate 8 t-shirts in 3 hours. At this rate, write and solve a proportion to find the time it will take him to decorate 20 t-shirts.

Write a proportion. Let t represent the time in hours.

shirts

timetime

shirts

Write and Solve a Proportion

Write the proportion.

Find the cross products.

Multiply.

Divide each side by 8.

Simplify.

Answer: It will take Melvin 7.5 hours to decorate 20 t-shirts.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 6.5 hours

B. 7 hours

C. 7.2 hours

D. 7.6 hours

CLOTHING Adrian can decorate 5 t-shirts in 2 hours. At this rate, write and solve a proportion to find the time it will take her to decorate 18 t-shirts.

COOKING A recipe serves 10 people and calls for 3 cups of flour. If you want to make the recipe for 15 people, how many cups of flour should you use?

Write a proportion. Let c represent the number of cups of flour needed to serve 15 people.

cups of flour

total people servedtotal people served

cups of flour

Answer: You will need 4.5 cups of flour to make the recipe for 15 people.

Find the cross products.

Multiply.

Divide each side by 10.

Simplify.

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. 6.5 cups

B. 6.7 cups

C. 7.2 cups

D. 7.5 cups

COOKING A recipe serves 12 people and calls for 5 cups of sugar. If you want to make the recipe for 18 people, how many cups of sugar should you use?

Write and Use an Equation

FOOD Haley bought 4 pounds of tomatoes for $11.96. Write an equation relating the cost to the number of pounds of tomatoes. How much would Haley pay for 6 pounds at this same rate? for 10 pounds?

Find the constant of proportionality between cost and pounds.

The cost is $2.99 per pound.

Write and Use an Equation

The cost is $2.99 times the number of pounds.Words

Let c represent the cost.Let p represent the number of pounds.

c = 2.99 ● p

Variable

Equation

Use this same equation to find the cost for 6 and 10 pounds of tomatoes sold at the same rate.

Write and Use an Equation

Answer: The cost for 6 pounds of tomatoes is $17.94 and for 10 pounds is $29.90.

Write the equation.

Replace p with the number of pounds.

Multiply.

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. $18.95

B. $19.20

C. $19.85

D. $20.15

FOOD Cameron bought 3 pounds of apples for $11.37. Write an equation relating the cost to the number of pounds of apples. How much would Cameron pay for 5 pounds at this same rate?

• TEETH: For every 6 people who say they floss daily, there are 14 people who say they do not. Write and Solve a proportion to determine out of 50 people how many you would expect to say they do floss daily.

• ILLNESS: For every person who actually has the flu, there are 5 people who have the same symptoms but with only a cold. If a doctor sees 60 patients, write and solve a proportion to determine how many of these you would expect to only have a cold.

• PHOTOGRAPHY: It takes 3 minutes to print out 4 digital photos. Write an equation relating the number of photos, n, to the number of minutes, m.

• At this rate, how long will it take to print 10 photos?