MathDB
Three Coupons

Source: 2010 AMC 10B Problem 11

February 25, 2010
AMC

Problem Statement

A shopper plans to purchase an item that has a listed price greater than $100 \$100 and can use any one of the three coupons. Coupon A gives 15% 15\% off the listed price, Coupon B gives $30 \$30 the listed price, and Coupon C gives 25% 25\% off the amount by which the listed price exceeds $100 \$100.
Let x x and y y be the smallest and largest prices, respectively, for which Coupon A saves at least as many dollars as Coupon B or C. What is y\minus{}x?
<spanclass=latexbold>(A)</span> 50<spanclass=latexbold>(B)</span> 60<spanclass=latexbold>(C)</span> 75<spanclass=latexbold>(D)</span> 80<spanclass=latexbold>(E)</span> 100 <span class='latex-bold'>(A)</span>\ 50\qquad<span class='latex-bold'>(B)</span>\ 60\qquad<span class='latex-bold'>(C)</span>\ 75\qquad<span class='latex-bold'>(D)</span>\ 80\qquad<span class='latex-bold'>(E)</span>\ 100