Official Guide Explanation:
Problem Solving #195

 

 

Background

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Solution and Metadata

Question: 195
Page: 180
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Ratio and Proportion >
Category 2: Word Problems > Rate Problems > other

Explanation: Say that the current price of the towels is x. That means that, when increased, the price of the towels will be x + 1. The number of towels that can be purchased for $120 when the price is x is (120/(x)), and the number of towels that can be purchased when the price is increased is (120/(x + 1)). Since 10 fewer towels can be purchased for $120 at the higher price, we can set up an equation:

(120/(x)) - 10 = (120/(x + 1))

((120 - 10x)/(x)) = (120/(x + 1))

(120 - 10x)(x + 1) = 120x

120x - 10x2 + 120 - 10x = 120x

-10x2-10x + 120 = 0

x2 + x - 12 = 0

(x + 4)(x - 3)

x = 3 or x= - 4

Since towels can't have negative prices, the price per towel must be $3, choice (C).

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