# Calculating the selling price of a house, given the mortgage, commission, and closing costs

I'm trying to help my wife study for her real estate exam, I thought I was good at math (although I haven't done any in years).

Here is the question at hand :

You sell a home for a client, and the client receives \$$20,000 in cash after she pays off the remainder of her mortgage. The mortgage was \80,000. She also paid four percent of the selling price in closing costs and another six percent in commissions. What did you sell the house for? I calculated that I sold the house for 110k, but apparently correct result is 111.000. The scoring web site didn't say why or explained the procedure, can somebody shed some light on this one? ## 3 Answers Ok, so you want to know how much you sold the house for. Since this is an unknown, let's call it x. So x represents how much you sold the house for. She paid 4 \% of the selling price in closing costs, so since x is the amount the house sold for, then 0.04x is the amount she paid in closing costs. She paid 6 \% of the selling price in commissions, so that means she paid 0.06x in commissions. So we have x is the selling price, and it is broken into four parts. The \$$20,000$she kept at the end, the \$$80,000 used to pay off her mortgage, and the two amounts 0.04x and 0.06x she paid. So the sum of these four amounts is equal to the total selling price, which is x. So we get the equation: x = 80,000 + 20,000 + 0.04x + 0.06x We want to solve for x by first moving all of the terms with x's to one side, so let's subtract 0.04x and 0.06x from both sides. We get: x - 0.04x - 0.06x = 100,000 And combining like terms on the left hand side, we get that: 0.9x = 100,000 Now, dividing both sides by 0.9 to solve for x, we get: x = \dfrac{100,000}{0.9} and this simplifies to x = 111,111.11 So the house sold for \$$111,111.11$ -- that is an oddly specific price!

• This is just a test question, thanks for the thorough explanation. I sent my wife this link. Thanks Aug 15, 2014 at 3:01
• @GandalfStormCrow You're welcome! :) Aug 15, 2014 at 3:01

Let $s$ be the selling price. You are told that $s=20,000+80,000+0.04s+0.06s$ Can you solve that? Mathematically, the answer is not $111,000$ either, but it is close.

Set up the equation:

$Money\ Left = Selling\ Price - Mortgage - Closing\ Costs - Commissions$

$\$20,000 = (Selling\ Price) - \$80,0000 - (Selling\ Price) \frac{4}{100} - (Selling\ Price) \frac{6}{100}$

Add the mortgage to both sides: $\$100,000 = (Selling\ Price) - (Selling\ Price) \frac{4}{100} - (Selling\ Price) \frac{6}{100}$Add the fractions:$\$100,000 = \frac{100 - 4 - 6}{100}(Selling\ Price)$

$\$100,000 = \frac{90}{100}(Selling\ Price)$Multiply both sides by$\frac{100}{90}\$100,000 * \frac{100}{90} = (Selling\ Price)$

Apply calculator:

$\$111,111.11$Apparently rounded to nearest$1K.