# Problem #2323

 2323 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 $\textdollar50$ Coupon 2: $\textdollar 20$ off the listed price if the listed price is at least $\textdollar100$ Coupon 3: $18\%$ off the amount by which the listed price exceeds $\textdollar100$ For which of the following listed prices will coupon $1$ offer a greater price reduction than either coupon $2$ or coupon $3$? $\textbf{(A) }\textdollar179.95\qquad \textbf{(B) }\textdollar199.95\qquad \textbf{(C) }\textdollar219.95\qquad \textbf{(D) }\textdollar239.95\qquad \textbf{(E) }\textdollar259.95\qquad$ This problem is copyrighted by the American Mathematics Competitions.
Note: you aren't logged in. If you log in, we'll keep a record of which problems you've solved.

• Reduce fractions to lowest terms and enter in the form 7/9.
• Numbers involving pi should be written as 7pi or 7pi/3 as appropriate.
• Square roots should be written as sqrt(3), 5sqrt(5), sqrt(3)/2, or 7sqrt(2)/3 as appropriate.
• Exponents should be entered in the form 10^10.
• If the problem is multiple choice, enter the appropriate (capital) letter.
• Enter points with parentheses, like so: (4,5)
• Complex numbers should be entered in rectangular form unless otherwise specified, like so: 3+4i. If there is no real component, enter only the imaginary component (i.e. 2i, NOT 0+2i).