Question

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

Answer 1

C. $215,000

Step-by-step explanation:

The statement indicates that on the first $50,000 the auction house charges 15%, which means that for the first $50,000 the house charged:

$50,000*0,15%= $7,500

From the total commission of $24,000, $7,500 were for the first $50,000.

$24,000-$7,500= $16,500

Now, you have to determine the amount in excess of $50,000 from which the house charged the remaining $16,500. So, you have that an x amount multiplied for 10% or 0,10 is equal to $16,500:

x*0,10= 16,500

x= 16,500/0,10= 165,000

You have determined that the house charged $7,500 on the first $50,000 and $16,500 on $165,000 which means that the price of the painting is:

$50,000+$165,000= $215,000