Percent - XYZ Custom Plus

314Chapter 5 PercentPractice Problems1. a. What number is 25% of 74?b. What number is 50% of 74?Example 1What number is 15% of 63?SolutionWe translate the sentence into an equation as follows:What number is 15% of 63?gg gg gn = 0.15 ⋅ 63To do arithmetic with percents, we have to change to decimals. That is why 15%is rewritten as 0.15. Solving the equation, we haven = 0.15 ⋅ 63n = 9.4515% of 63 is 9.452. a. What percent of 84 is 21?b. What percent of 84 is 42?Example 2What percent of 42 is 21?SolutionWe translate the sentence as follows:What percent of 42 is 21?n ⋅ 42 = 21We solve for n by dividing both sides by 42._​ n ⋅ ​ 42​ ​= ​_2142​ ​ 42 ​n = ​_2142 ​n = 0.50Because the original problem asked for a percent, we change 0.50 to a percent:n = 50%21 is 50% of 42ggg g g3. a. 35 is 40% of what number?b. 70 is 40% of what number?Example 325 is 40% of what number?SolutionFollowing the procedure from the first two examples, we have25 is 40% of what number?g gg25 = 0.40 ⋅ nAgain, we changed 40% to 0.40 so we can do the arithmetic involved in the problem.Dividing both sides of the equation by 0.40, we have_​ 250.40 ​= ​​ _ 0.40​⋅ n​​ 0.40​_​ 250.40 ​= n62.5 = ng25 is 40% of 62.5gAnswers1. a. 18.5 b. 372. a. 25% b. 50%3. a. 87.5 b. 175As you can see, all three types of percent problems are solved in a similar manner.We write is as =, of as ⋅, and what number as n. The resulting equation is thensolved to obtain the answer to the original question.