AMC 12 2014a Problem 8

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 $3$?

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