2010 AMC 10B Problem 11

A shopper plans to purchase an item that has a listed price greater than \$100 and can use any one of the three coupons. Coupon A gives 15\% off the listed price, Coupon B gives \$30 off the listed price, and Coupon C gives 25\% off the amount by which the listed price exceeds \$100.
Let x and y be the smallest and largest prices, respectively, for which Coupon A saves at least as many dollars as Coupon B or Coupon C. What is y - x?

\textbf{(A)}\ 50 \qquad \textbf{(B)}\ 60 \qquad \textbf{(C)}\ 75 \qquad \textbf{(D)}\ 80 \qquad \textbf{(E)}\ 100

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.