590 CHAPTER 10 Consumer Mathematics 2. If Nancy sells a car for $19,000 and receives a commission of $475, what percent of the sale price is the commission? The problem can be restated as What percent of $19,000 is $475? 3. If the price of a laptop computer is reduced by 35% or $341.25, what was the original price of the computer? The problem can be restated as 35% of what number is $341.25? To answer these three questions, we will translate the words of the problem into an equation and then solve the equation. Some common words or phrases that we encounter are shown below, along with the symbols used when writing the equation. Word or phrase Symbol in the equation what number x what percent x is, are, was, or were = of ⋅ To solve each problem given, we change the percent into a decimal number and change the words of the sentence into symbols of an equation. We then solve the equation for x. 1. 15% of $45.71 is what number? x x x 0.15 45.71 0.15 45.71 6.8565 ⋅ = ⋅ = = Since 15% of $45.71 is $6.8565, the tip would be $6.86. 2. What percent of $19,000 is $475? x x x x 19,000 475 19,000 475 19,000 475 475 19,000 0.025 2.5% ⋅ = ⋅ = = = = = Since 2.5% of $19,000 is $475, the commission is 2.5% of the sale price. 3. 35% of what number is $341.25? x x x x 0.35 341.25 0.35 341.25 0.35 341.25 341.25 0.35 975 ⋅ = ⋅ = = = = Since 35% of $975 is $341.25, the original price of the computer was $975. ()* " (+)+* " (++)++* (++)++* " (+)+* " (+)+* ()* " (++)++* " (+)+* Example 9 Down Payment on a Condominium Melissa wishes to buy a condominium selling for $189,000. To obtain the mortgage loan, she must pay 20% of the selling price as a down payment. a) Determine the amount of Melissa’s down payment. b) Determine the amount of the mortgage loan.
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