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?

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.