smc

Question

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?

Accepted Answer

Let the listed price be x. Since all the answer choices are above 100, we can assume x > 100. Thus the discounts after the coupons are used will be as follows: Coupon 1: x10%=.1x Coupon 2: 20 Coupon 3: 18%(x-100)=.18x-18 For coupon 1 to give a greater price reduction than the other coupons, we must have .1x>20 x>200 and .1x>.18x-18.08x<18 x<225. The only choice that satisfies such conditions is 219.95