This document provides examples and explanations for solving percent problems using equations. It discusses finding percentages, parts, and wholes. Examples are provided such as finding 15% of 40, 45.5% of 20, and commissions on real estate sales. It also discusses using equations to solve word problems involving percentages such as royalties on CD sales and survey results.

1. Chapter 6, Section 7: Percents and Equations December 15, 2008

2. Warm-Up Is OVER Of . What percent OF 35 IS 5? X/100 = % X/100 = 5/35 5/35 Is = 5 OVER Of = 35 35X = 5(100) 35X = 500 X = 14.2%

3. Warm Up From Quiz Three way to write a ratio: a:b, a/b, a to b . A PROPORTION is an equality of two ratio. Two figures are SIMILAR if they have corresponding angles and corresponding sides. PROBABILITY compares favorable outcomes to total possible outcomes. “ Odds in favor ” describes the relation between favorable outcomes to unfavorable outcomes. Where as, “ odds against ” describes the relation between unfavorable to favorable outcomes. A number over 100 (#/100) is another way of writing A PERCENT .

4. Writing and Solving Percent Equations Solve a Percent problem by writing and solving an equation. When you use a percent in an equation, write it as a decimal.

5. Finding The Percent What Percent Of 40 is 6? N • 40 = 6 N = 6 /40 N = 0.15 N = 15% Equation The unknown is the percent TIMES the whole. 6 is the percentage of the whole.

6. Finding the Part What is 15% of 40? N = 0.15 • 40 N = 0.15 • 40 N = 6 6 is 15% of 40 Equation The unknown is 15% of 40. 6 is the PART of 40 40 is the whole.

7. Finding the Whole 6 is 15% of what? 6 = .15 • N 6/.15 = N 40 = N 6 is 15% of 40 Equation The unknown is the whole here. 6 is 15% of a whole that we don’t know.

8. What is 85% of 62? 1 st : What are we looking for? Percent, Part, or Whole? 2 nd : Looking for Part: Write an equation, with the Percent as a Decimal. N = .85 • 62 Simplify: N = 52.7 85% of 62 is 52.7 (52.7 = Part of 62)

9. This Works For Percentages Greater Than 100 As All. What percent of 48 is 54? What are we looking for? Write an Equation. N • 48 = 54 Simplify: N = 54/48 = 1.125 Move the Decimal point 2 times. N = 112.5%

10. Write an Equation and Solve It What is 45.5% of 20? 380 is 125% of what number? N = 0.455 • 20, N = 9.1 380 = 1.25 • N , N = 304

11. Using Equations to Solve Percent Problems Commission: The amount of money a job pays you based on how much you sell. REAL LIFE FOLKS! A real estate agent makes a 4.5% commission on property she sells. How much does she make on the sale of a house for $245,000?

12. Real Estate Game of Life A real estate agent makes a 4.5% commission on property she sells. How much does she make on the sale of a house for $245,000? 1 st : Percent, Part or Whole? 2 nd : Write an Equation. 3 rd : Simplify and Solve. Amount of Commission IS 4.5% OF $245,000 C Commission = .045 X $245,000 Commission, C = $11,025.00

13. Elvis Lives! If Elvis was alive when CDs were invented he would receives 5% of royalty on each CD sale. To the nearest cent, find Elvis’s royalty for each CD that sells for $16.99. The singer makes $0.85 off of each CD sale.

14. Peanut Butter In a survey, 922 people, or about 68.6%, preferred smooth peanut butter to chunky. How many people were surveyed? 1,344 people were surveyed.

15. Assignment #48 Page 312-313: 7-20 all. 31-36 all. Make sure you complete ALL parts of each problem!