At a sporting goods store, Jay paid $172 for a pair of shoes and a pair of pants. The pants cost less than two thirds of what the shoes cost. What is the minimum price of the shoes to the nearest dollar?
Correct answer: A. 103
- A. 103
- B. 110
- C. 120
- D. 90
Explanation
Let x be the price of the shoes and y be the price of the pants. Then we have: x + y = 172 ...(1) y < (2/3)x ...(2) To find the minimum price of the shoes, we need to maximize the price of the pants. From equation (1), we get: y = 172 - x Substituting this value of y in equation (2), we get: 172 - x < (2/3)x Multiplying both sides by 3, we get: 516 - 3x < 2x Adding 3x to both sides, we get: 516 < 5x Dividing both sides by 5, we get: x > 103.2 Rounding up to the nearest dollar, we get: x > 103 Therefore, the minimum price of the shoes to the nearest dollar is $103. Answer: A) 103.
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Quantitative reasoning applies arithmetic and basic algebra to numerical relationships, including percentages, ratios, averages, fractions, proportions, profit and loss, rates, time, work and measurement. Questions focus on translating words into equations, choosing an efficient method and checking whether the result is numerically reasonable.
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