Question

You are about to list your house as For Sale By Owner. Suppose you need to allow

for a 3% commission for the buyer's realtor, and you need to receive a minimum of
$92,500 on the sale. What is the minimum price you can list the house at to
accommodate both of these requirements? Round to the nearest hundred dollars.

$89,725

$95,275

$95,400

$95,000

Answer 1

(c) $95,400

Explanation:

You want the listing price of your house such that you can clear $92,500 after paying a 3% commission to the buyer's realtor.

Setup

The buyer's agent will receive 3% of the sale price (P), so you receive that amount less. You want your share to be $92,500.

(1 -3%)P = 92,500

Solution

Dividing by the coefficient of P, we get ...

P = 92,500/0.97 ≈ 95,361

We are asked to round this value to the nearest $100. That makes the listing price ...

$95,400 . . . . listing price

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Additional comment

You can estimate the listing price by adding 3% of 92500 to that value, and you can estimate the added amount as 3%×90,000 = 2700. That is, you know the listing price needs to be slightly higher than ...

92500 +2700 = 95,200

Only one of the answer choices is above that value and rounded to the nearest $100. (You can eliminate the first two choices, because they are not properly rounded.)