BTGmoderatorDC wrote: ↑

Sun Jul 10, 2022 9:40 pm

For a long time, the price of a certain console remained the same. Because of new tariffs, the price of this console increased by 50% last week, and stayed at this new level. This week, Amanda purchased the console with a 50%-off coupon. Amanda paid $240. What was the original price, before the last week's price increase?

A. 90
B. 180
C. 240
D. 320
E. 360


OA D

Source: Magoosh

Let x = the original price of the console (in dollars)

Because of new tariffs, the price of this console increased by 50% last week
The new price = x + (50% of x) = x + 0.5x = 1.5x

Amanda purchased the console with a 50%-off coupon. Amanda paid $240
Purchase price = 50% of 1.5x
= (0.5)(1.5x) = 0.75x

Since Amanda paid $240 we can write: 0.75x = 240

ASIDE: If you'd rather not divide 240 by 0.75, you can rewrite the above equation as follows: (3/4)x = 240
From here we can eliminate the fraction by multiplying both sides of the equation by 4/3 to get: (4/3)(3/4)x = (4/3)(240)
Simplify: x = 320

Answer: D