That's a lot of words for such a straightforward setup. When he pays back half of the additional 15% discount, he is paying back 7.5% of the original price of the item. So $40.50 is 7.5% of the original price, and doubling everything, $81 is 15% of the original price. Of course we could do algebra here, but glancing at the answers, we can see D must be right, since $81 is 20% of answer C and 10% of answer E (so the right answer must be in between C and E).

BTGmoderatorDC wrote:George bought a large electronic item with a 15% off coupon, and paid a total bill. When he got outside, he studied the receipt and realize that he mistakenly had been given double the discount of the coupon, even though there was no double-coupon offer in effect that day. He went back inside and pointed this mistake out to the manager, offering to make the the difference between what he paid and what he should have paid. The manager was so grateful for George's honesty that he allowed George to pay just half that difference, so George paid him $40.50. What was the original price of the item, before any coupons? Assume that there was no tax at all in this scenario.


A) $135
B) $270
C) $405
D) $540
E) $810

OA D

Source: Magoosh

We can let the original price of the item = x dollars. After 15% off, and had the sale been done correctly, George should have paid 0.85x dollars. However, because of the mistake, he received 30% off, so he actually paid 0.7x dollars. Therefore, the difference is 0.85x - 0.7x = 0.15x dollars, which he should pay back to the store. However, since the manager allowed him to pay half the difference, which amounts to $40.50, we can create the equation

½(0.15x) = 40.5

0.15x = 81

x = 81/0.15 = 540

Alternate Solution:

The $40.50 payment that George paid back to the store represents half of the 15% discount, which is 7.5%. Thus, if we let x = the original price of the item, we can create the following equation:

0.075x = 40.5

75x = 40,500

x = 540

Answer: D