### Brain Teasers

# Ann And Real Estate

Ann purchased a house for $166,902. She wants to sell it for a profit of exactly 13%. However, she does not want to sell it herself. She wants a Real Estate Agent to sell it for her. The Agent must make a commission of exactly 5.7% (in addition to Ann's 13% profit). How much must the Agent sell the house for? Give your answer to the nearest dollar.

### Answer

The Agent must sell Ann's house for $ 200000.The Agent gets $ 11400 as commission (i.e., 0.057 x 200000).

Ann gets (including profit) $ 188600, i.e., 200000 - 11400.

It may be noted that: (188600 - 166902) / 166902 x 100 = 13%.

Importantly, profit is calculated on purchase cost (by Ann) and commission is calculated on selling price (by the Agent).

The problem may also be solved by setting up the following equation:

Purchase Cost + Ann's Profit + Agent's Commission = Selling Price

166902 + (13/100) 166902 + (5.7/100) S = S

where S is the Selling Price in $.

The equation may be solved as shown below.

188600 + 0.057 S = S

S = 188600 / (1 - 0.057) = 200000.

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