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Bell Work: Find the product (7.5 x 10 )(2 x 10 )

In this lesson, we learn how to solve percent problems using proportions or by solving a percent equation. We practice converting percentages to decimals or fractions and using them to find unknown numbers. We also solve real-life percent problems.

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Bell Work: Find the product (7.5 x 10 )(2 x 10 )

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  1. Bell Work: Find the product (7.5 x 10 )(2 x 10 ) -3 -4

  2. Answer: 1.5 x 10 -6

  3. Lesson 58:Solving Percent Problems with Equations

  4. We may solve percent problems using proportions (as we did in Lesson 48) or by solving a percent equation.

  5. A percent of a whole is a part. % x W = P

  6. The factors and product in the equation before are the percent, the whole, and the part. If two of the three numbers are known, we can write and solve an equation to find the unknown number.

  7. If we are given the percent, we convert the percent to a fraction or decimal before performing the calculation.

  8. For any percent problem we may choose to express the percent as a decimal or as a fraction. We might make the choice based on which form seems easier to calculate.

  9. For some problems the calculations are tedious, so we might choose to express the percent as a decimal and use a calculator. For other problems, expressing the percent as a fraction is the best choice.

  10. Example: Thirty-two ounces is 25% of a gallon. How many ounces is a gallon?

  11. Answer: As a decimal: As a fraction: 32 oz. is 25% of a gal. 32 = 0.25g 32 = 1/4g 32/.25 = g 32x4 = g g = 128 g = 128 128 ounces

  12. Practice: Mr. Villescas bought a used car for $8,500. the sales-tax was 7%. How much did Mr. Villescas pay in tax?

  13. Answer: As a Decimal: As a Fraction: Tax is 7% of price t = 0.07 x $8500 t = 7/100 x 8500 t = $595 t = $595

  14. Practice: For the following percent problems, decide whether it is better to express the percent as a decimal or as a fraction. • The sales-tax rate was 8.25%. What was the sales tax on a $18.97 purchase? • Shirts are on sale for 33 1/3% off the regular price. How much is saved on a $24 shirt?

  15. Answer: a) To calculate an exact answer we would convert the percent to a decimal and use a calculator.

  16. Answer: b) To write the percent as a decimal we would need to round. Expressing the percent as a fraction 1/3 is more accurate, we can perform the calculation mentally. We would express the percent as a fraction.

  17. Practice: Blanca correctly answered 23 of the 25 questions. What percent of the questions did she answer correctly?

  18. Answer: What percent of 25 is 23? P x 25 = 23 P = 23/25 = 0.92 P = 92%

  19. HW: Lesson 58 #1-30

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