An electronics store purchases a certain video game from the manufacturer, but in a mass amount of clutter the original purchase price is lost. The store sells the game at a mark-up of 200% over the purchase price. A coupon which the store offers in the local newspaper will reduce the price by 20%. With the coupon, the profit made on the sale of the video game is $18. What was the original purchase price of the video game? Give your answer as a decimal rounded to the nearest hundredth.
A) $8.00
B) $16.25
C) $12.45
D) $12.86
E) None of the above.

Question

An electronics store purchases a certain video game from the manufacturer, but in a mass amount of clutter the original purchase price is lost. The store sells the game at a mark-up of 200% over the purchase price. A coupon which the store offers in the local newspaper will reduce the price by 20%. With the coupon, the profit made on the sale of the video game is $18. What was the original purchase price of the video game? Give your answer as a decimal rounded to the nearest hundredth. 
A) $8.00
B) $16.25
C) $12.45
D) $12.86
E) None of the above.

Quizplus · Accepted Answer

Let $x$ be the original purchase price. The store sells the game at a 200% markup, so the selling price is $x + 2x = 3x$. A 20% discount on the selling price is $0.8 \times 3x = 2.4x$. The profit with the coupon is thus $2.4x - x = 1.4x = $18$. Solving for $x$, we get $x = \frac{18}{1.4} = 12.8571$, which rounds to $12.86.

An Electronics Store Purchases a Certain Video Game from the Manufacturer