1. 7
Percent

2. R.1 Fractions
7.4 Problem Solving with Percent
Objectives
Solve percent application problems.
Solve problems involving percent of increase or decrease.

3. Solve percent application problems.
A new low-income housing project charges 30% of a family’s income as rent. The Smiths’ family income is $1260 per month. How much will the Smiths pay for rent?
Example
Step 1 Read the problem.
Unknown: amount of rent
Known: 30% of income paid for rent; $ monthly income
Step 2 Assign a variable. There is only one unknown, so let n be the amount paid for rent.

4. Solve percent application problems.
(continued)
Example
Step 3 Write an equation. Use the percent equation.
Step 4 Solve the equation.

5. Solve percent application problems.
(continued)
Example
Step 5 State the answer.
The Smith family will pay $378 for rent.
Step 6 Check the solution.
The solution of $378 makes sense because 10% of $1260 is $126, so 30% would be 3 times $126, or $378.

6. Solve percent application problems.

7. Solve percent application problems.
When Britta received her first $180 paycheck as a math tutor, was withheld for federal income tax. How much was withheld?
Example
Step 1 Read the problem.
Unknown: amount withheld for taxes
Known: of earnings withheld; $180 in pay
Step 2 Assign a variable. There is only one unknown, so let n be the amount withheld for taxes.

8. Solve percent application problems.
(continued)
Example
Step 3 Write an equation. Use the percent equation.
Step 4 Solve.

9. Solve percent application problems.
(continued)
Example
Step 5 State the answer.
$22.50 was withheld from Britta’s paycheck.
Step 6 Check the solution.
The solution of $22.50 makes sense because 10% of $180 is $18, so a little more than $18 should be withheld.

10. Solve percent application problems.
On a 15-point quiz, Zenitia earned 13 points. What percent correct is this, to the nearest whole percent?
Example
Step 1 Read the problem.
Unknown: percent correct
Known: earned 13 out of 15 points
Step 2 Assign a variable.
Let p be the unknown percent.

11. Solve percent application problems.
(continued)
Example
Step 3 Write an equation. Use the percent equation.
Step 4 Solve.

12. Solve percent application problems.
(continued)
Example
Step 5 State the answer.
Zenitia had 87% correct, rounded to the nearest whole percent.
Step 6 Check the solution.
The solution of 87% makes sense because she earned most of the possible points, so the percent should be fairly close to 100%.

13. Solve percent application problems.
The rainfall in the Red River Valley was 33 inches this year. The average rainfall is 30 inches. This year’s rainfall is what percent of the average rainfall?
Example
Step 1 Read the problem.
Unknown: This year’s rain is what percent of the average?
Known: 33 inches this year; 30 inches is average
Step 2 Assign a variable.
Let p be the unknown percent.

14. Solve percent application problems.
(continued)
Example
Step 3 Write an equation.
Step 4 Solve.

15. Solve percent application problems.
(continued)
Example
Step 5 State the answer.
This year’s rainfall is 110% of the average rainfall.
Step 6 Check the solution.
The solution of 110% makes sense because 33 inches is more than 30 inches (more than 100% of the average rainfall), so 33 inches must be more than 100% of 30 inches.

16. Solve percent application problems.
A newspaper article stated that 648 pints of blood were donated at the blood bank last month, which was only 72% of the number of pints needed. How many pints of blood were needed?
Example
Step 1 Read the problem.
Unknown: number of pints needed
Known: 648 pints were donated;
648 pints is 72% of the number needed.
Step 2 Assign a variable.
Let n be the number of pints needed.

17. Solve percent application problems.
(continued)
Example
Step 3 Write an equation.
Step 4 Solve.

18. Solve percent application problems.
(continued)
Example
Step 5 State the answer.
900 pints of blood were needed.
Step 6 Check the solution.
The solution of 900 pints makes sense because 10% of 900 pints is 90 pints, so 70% would be 7 times 90 pints, or 630 pints, which is close to the number given in the problem (648 pints).

19. Solve problems involving percent of increase or decrease.

20. Solve problems involving percent of increase or decrease.
Brad’s hourly wage as assistant manager of a fast-food restaurant was raised from $9.40 to $9.87. What was the percent of increase?
Example
Step 1 Read the problem.
Unknown: percent of increase
Known: Original hourly wage was $9.40;
new hourly wage is $9.87.
Step 2 Assign a variable.
Let p be the percent of increase.

21. Solve problems involving percent of increase or decrease.
(continued)
Example
Step 3 Write an equation.
Step 4 Solve.

22. Solve problems involving percent of increase or decrease.
(continued)
Example
Step 5 State the answer.
Brad’s hourly wage increased 5%.
Step 6 Check the solution.
10% of $9.40 would be a $0.94 raise. A raise of $0.47 is half as much, and half of 10% is 5%, so the solution checks.

23. Solve problems involving percent of increase or decrease.

24. Solve problems involving percent of increase or decrease.
Rozenia trained for six months to run in a marathon. Her weight dropped from 137 pounds to 122 pounds. Find the percent of decrease. Round to the nearest whole percent.
Example
Step 1 Read the problem.
Unknown: percent of decrease
Known: Original weight was 137 pounds;
new weight is 122 pounds.
Step 2 Assign a variable.
Let p be the percent of decrease.

25. Solve problems involving percent of increase or decrease.
(continued)
Example
Step 3 Write an equation.
Step 4 Solve.

26. Solve problems involving percent of increase or decrease.
(continued)
Example
Step 5 State the answer.
Rozenia’s weight decreased approximately 11%.
Step 6 Check the solution.
A 10% decrease would be 13.7 pounds,
so an 11% decrease is a reasonable solution.