2014 AMC 10A Problem 11

A customer who intends to purchase an appliance has three coupons, only one of which may be used:

Coupon 1: 10\% off the listed price if the listed price is at least \$50

Coupon 2: \$20 off the listed price if the listed price is at least \$100

Coupon 3: 18\% off the amount by which the listed price exceeds \$100

For which of the following listed prices will coupon 1 offer a greater price reduction than either coupon 2 or coupon 3?

\textbf{(A) }\$179.95\qquad \textbf{(B) }\$199.95\qquad \textbf{(C) }\$219.95\qquad \textbf{(D) }\$239.95\qquad \textbf{(E) }\$259.95\qquad

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