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Solve percent problems using percent equations. You have already used the percent proportion to solve problems. (Lesson 7–3) Solve percent problems using percent equations. Apply the percent equation to real-world problems. Then/Now

Find the Part Find 38% of 22. Estimate 40% of 20 is 8. Example 1

n = 0.38 • 22 Write the percent equation. Find the Part n = 0.38 • 22 Write the percent equation. = 8.36 Multiply. Answer: 38% of 22 is 8.36. Check for Reasonableness 8.36 ≈ 8  Example 1

Find 64% of 48. A. 32 B. 75 C. 30.72 D. 30 Example 1

The whole is 25 and the part is 19. Let n represent the percent. Find the Percent 19 is what percent of 25? Estimate The whole is 25 and the part is 19. Let n represent the percent. Write the percent equation. Divide each side by 25. Example 2

Check for Reasonableness 76% ≈ 80%  Find the Percent 0.76 = n Simplify. By definition, the percent is expressed as a decimal. Convert 0.76 to a percent. Answer: 19 is 76% of 25. Check for Reasonableness 76% ≈ 80%  Example 2

8 is what percent of 25? A. 312% B. C. 32% D. 2% Example 2

The part is 84 and the percent is 16%. Let n represent the whole. Find the Whole 84 is 16% of what number? 84 is 16% of what number? Estimate 80 is 16% of 500. The part is 84 and the percent is 16%. Let n represent the whole. Write 16% as the decimal 0.16. Divide each side by 0.16. Example 3

Check for Reasonableness 525 ≈ 500  Find the Whole 525 = n Simplify. Answer: So, 84 is 16% of 525. Check for Reasonableness 525 ≈ 500  Example 3

315 is 42% of what number? A. 750 B. 132.3 C. 13.33 D. 150 Example 3

Concept

Method 1 Find the tax first. Then add. Use the Percent Equation SALES TAX Chan wants to buy a cell phone that costs $180. If a 7% sales tax is added, what is the total cost? Method 1 Find the tax first. Then add. The whole is $180. The percent is 7%. You need to find the amount of the tax, or the part. Let t represent the amount of tax. t = 0.07 ● 180 Write 7% as a decimal. t = 12.60 Multiply. The tax is $12.60. The total cost is $180 + $12.60 or $192.60. Example 4

Method 2 Find the total percent first. Use the Percent Equation Method 2 Find the total percent first. Find 100% + 7% or 107% of $180 to find the total cost, including tax. t = 1.07 ● 180 Write 107% as a decimal. t = 192.60 Multiply. Answer: Using either method, the total cost is $192.60. Example 4

The sales tax on a bicycle is 5% The sales tax on a bicycle is 5%. If the price of the bicycle is $126, what is the total cost? A. $126.05 B. $132.30 C. $138.60 D. $163.00 Example 4

You are asked to find the estimated percent of sales tax. Mr. Wilkins purchased a DVD player for $97.19 including tax. The DVD player had a sticker price of $89.99. About what percent sales tax did he pay? A 6% B 7% C 8% D 9% Read the Test Item You are asked to find the estimated percent of sales tax. Example 5

7.20 = p ● 89.99 Write the percent equation. Solve the Test Item The tax is $97.19 – $89.99 or $7.20. 7.20 = p ● 89.99 Write the percent equation. Divide each side by 89.99. 0.08  p Simplify. 0.08 = 8% Answer: The correct answer is C. Example 5

Jeanne bought a DVD for $18. 18 including tax Jeanne bought a DVD for $18.18 including tax. The sticker price of the DVD was $16.99. About what percent sales tax did she pay? A. 5% B. 6% C. 7% D. 8% Example 5

End of the Lesson