1. 1 Astronomy On June 14, 2002, the distance between Earth and the moon was about 375,000 kilometers. On that day, a traveling asteroid missed Earth by about 32% of that distance. How far away from Earth was the asteroid at that time? The Percent Equation 7.4 LESSON

2. 2 You have used the proportion = to solve percent problems. When you solve this proportion for a and write as p%, you get the equation a = p% b. a b p 100 p The Percent Equation 7.4 LESSON

3. 3 The Percent Equation You can represent “ a is p percent of b ” using the equation a = p% b where a is a part of the base b and p% is the percent. The Percent Equation 7.4 LESSON

4. 4 Finding a Part of a Base EXAMPLE 1 To find how far away from Earth the asteroid was, use the percent equation. a = p% b Write percent equation. = 32% 375,000 = 0.32 375,000 Write percent as a decimal. = 120,000 ANSWER The asteroid was about 120,000 kilometers away from Earth. Substitute 32 for p and 375,000 for b. Multiply. The Percent Equation 7.4 LESSON

5. 5 Finding a Commission EXAMPLE 2 Commission A car salesperson earns a 6.5% commission on every car sold. The salesperson sells a car for $21,800. What is the commission? a = p% b Write percent equation. = 6.5% 21,800 = 0.065 21,800 Write percent as a decimal. = 1417 ANSWER The salesperson’s commission is $1417. Substitute 6.5 for p and 21,800 for b. Multiply. SOLUTION The Percent Equation 7.4 LESSON

6. 6 Finding a Percent EXAMPLE 3 What percent of 25 is 60 ? a = p% b Write percent equation. 60 = p% 25 2.4 = p% Divide each side by 25. 240% = p% ANSWER 60 is 240% of 25. Substitute 60 for a and 25 for b. Write decimal as a percent. The Percent Equation 7.4 LESSON

7. 7 Finding a Base EXAMPLE 4 Movies Your friend paid $9 for a movie ticket. This amount was 72% of the total amount your friend spent at the theater. How much money did your friend spend? a = p% b Write percent equation. 9 = 72% b 9 = 0.72 b Write percent as a decimal. 12.5 = b ANSWER Your friend spent $12.50 at the theater. Substitute 9 for a and 72 for p. Divide each side by 0.72. The Percent Equation 7.4 LESSON

8. 8 Methods for Solving a Percent Problem SUMMARY To find the percent of a number: Write the percent as a fraction.Write the percent as a decimal. Example: 5% of 16 = 0.05 16 = 0.8 20% of 35 = 35 = 7 1 5 The Percent Equation 7.4 LESSON

9. 9 Methods for Solving a Percent Problem SUMMARY To find the percent of a number: Write the percent as a fraction.Write the percent as a decimal. Example: 5% of 16 = 0.05 16 = 0.820% of 35 = 35 = 7 1 5 To find the percent p%, the base b, or a part a of the base: Use the proportionUse the percent equation Example: 21 is 35% of what number?What percent of 250 is 40 ? a = p% b. a b p 100 =. 21 b 35 100 = 60 = b 40 = p% 250 16% = p% The Percent Equation 7.4 LESSON