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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?

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3 Answers 3

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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!

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

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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.

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