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?
 A: 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!
A: 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.
A: 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.
