In auction house charges a commission of 15% on the first $50,000 of the sale price of an item...

[AAPL]

GMAT Prep

An auction house charges a commission of 15% on the first $50,000 of the sale price of an item, plus 10% on the amount of the sale price in excess of $50,000. What was the price of a painting for which the house charged a total commission of $24,000?

A. $115,000
B. $160,000
C. $215,000
D. $240,000
E. $365,000

OA C

[Scott@TargetTestPrep]

GMAT Prep

An auction house charges a commission of 15% on the first $50,000 of the sale price of an item, plus 10% on the amount of the sale price in excess of $50,000. What was the price of a painting for which the house charged a total commission of $24,000?

A. $115,000
B. $160,000
C. $215,000
D. $240,000
E. $365,000

OA C

Solution:

We can create the equation where p is the price of the item:

0.15 x 50,000 + 0.1 x (p - 50,000) = 24,000

7,500 + 0.1p - 5,000 = 24,000

0.1p + 2,500 = 24,000

0.1p = 21,500

p = 21,500/0.1 = 215,000

Answer: C