Base: The number that represents the whole or 100%. Amount: The number that represents part of a whole. Percent: The number that defines what part the amount is of the whole. B = Base A = Amount P = percent Percent Equation: Percent  Base = Amount or P  B = A Procedure: Solving Percent Problems using a Percent Equation: 1. Percents must be converted to a decimal or a fraction. 2. “what percent”: percent is unknown “of what number”: base is unknown “is what number”: amount is unknown 3. Substitute the values given into the percent equation. One of the values will not be given; either P, B, or A. 4. Solve the equation. If finding a percent, convert the decimal to a percent. Example 1. 75% of what number is 60. Solution: 1. List the given information. P=0.75 B=? A = 60 Equation: P  B = A 2. Substitute the information into the equation and solve. 0.75  B = 60 Your Turn Problem #1 20% of what number is 18? 0.75 0.75 Answer: 90 B = 80 75% of 80 is 60.

Example 2. 105 is what percent of 140? 1. List the given information. Solution: P=? B=140 A = 105 Equation: P  B = A 2. Substitute the information into the equation and solve. P  140 = 105 140 140 P = 0.75 Division not shown Your Turn Problem #2 81 is what percent of 540? P = 75% 105 is 75% of 140. Answer: 15% Example 3. 14% of 28 is what number? Solution: P=0.14 B=28 A =? Equation: P  B = A 1. List the given information. 0.14 28 = A 2. Substitute the information into the equation and solve. 14% of 28 is 3.92. A = 3.92 Multiplication not shown Your Turn Problem #3 5% of 180.2 is what number? Answer: 9.01

Solution: P = 2/9 B=? A =46 Equation: P  B = A B = 207 1. P must be written as a decimal or a fraction. 2. List the given information. P = 2/9 B=? A =46 Equation: P  B = A 3. Substitute the information into the equation and solve. To solve an equation with a fraction in front of the variable, multiply both sides by its reciprocal on both sides. B = 207 22 2/9% of 207 is 46. Your Turn Problem #4 Answer: 174

Solving Percent Problems using Proportions This is another method for solving percent problems. 1. The percent will not need to be converted to a decimal or a fraction (because of the 100 in the formula). 2. Substitute the values given in into the formula and solve the equation. Example 5. 31% of what number is 6975? Solution: P = 31 B= ? A = 6975 1. List the given information. 2. Substitute the information into the formula and solve. Your Turn Problem #5 548 is what percent of 2740? Answer: 20% The End B.R. 6-6-08 31B = 697500 B = 22,500