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
For a long time, the price of a certain console remained the same. Because of new tariffs, the price of this console
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Let x = the original price of the console (in dollars)BTGmoderatorDC wrote: ↑Sun Jul 10, 2022 9:40 pmFor 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
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