1. Solving Percents Using Proportions
Lesson 16
Proportionality
Solving Percents Using Proportions

2. Warm-Up Solve each proportion.1 3 5 7 9 10 15 20
miles
Number of Students
Warm-Up
Solve each proportion.
Jamal organized a fundraiser that required students to earn money for running miles around the track on a Saturday. The histogram above shows the number of students who ran various intervals of miles.
How many students ran in the fundraiser?
Which mile range represents the largest group?
Find the probability that a randomly chosen student from the fundraiser ran at least 5 miles but less than 10 miles.

3. Solving Percents Using Proportions
Targets:
Find the percent of a number using proportions.
Find a missing number using proportions with percents.

6. Solve Percent Problems Using Proportions
To find the percent, part or whole value for numbers in a
percent problem:
Write the percent as a ratio.
Write the ratio for the part of a number to its whole value.
Write a proportion using the ratios from Steps 1 and 2.
Solve the proportion.

7. Example 1 What is 24% of 75? Write the proportion.
Use cross products to solve x = 1800
x = 18
18 is 24% of 75.

8. Example 2 Thirty-one is 62% of what number? Write the proportion.
Use cross products to solve x = 3100
x = 50
31 is 62% of 50.

9. Example 3 What percent of 40 is 18? Write the proportion.
Use cross products to solve = 40x
x = 45
45% of 40 is 18.

10. Example 4 In 2006, people over the age of 65 made up 13% of the
population in Oregon. The total population in Oregon in 2006
was approximately 3,700,000. Find the number of people
over 65.
Write the percent as a fraction.
Write a proportion.
Use cross products to solve x = 48,100,000
x = 481,000
There were approximately 481,000 people over 65.

11. Exit Problems What is 20% of 60? What percent of 84 is 42?
Sixteen is 25% of what number?

12. Communication Prompt
When have you or someone you know used a percent to calculate a discount? How did you do it?