2007 AMC 12A Problems/Problem 5

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The following problem is from both the 2007 AMC 12A #5 and 2007 AMC 10A #7, so both problems redirect to this page.

Problem

Last year Mr. Jon Q. Public received an inheritance. He paid $20\%$ in federal taxes on the inheritance, and paid $10\%$ of what he had left in state taxes. He paid a total of $\textdollar10500$ for both taxes. How many dollars was his inheritance?

$(\mathrm {A})\ 30000 \qquad (\mathrm {B})\ 32500 \qquad(\mathrm {C})\ 35000 \qquad(\mathrm {D})\ 37500 \qquad(\mathrm {E})\ 40000$

Solution 1

After paying his taxes, he has $0.8*0.9=0.72$ of his earnings left. Since $10500$ is $0.28$ of his income, he got a total of $\frac{10500}{0.28}=37500\  \mathrm{(D)}$.

Solution 2

Let his total inheritance be a number $x$. The amount of tax he has to pay at first can be represented as $0.2x$. The amount of money he has left over after this expense can be written as $0.8x$. He then has to pay $10\%$ tax on this remaining amount, which can be written as $0.1(0.8x) = 0.08x$. The combined expense of these taxes is $10500$, so $0.2x + 0.08x = 10500 \Longrightarrow 0.28x = 10500$. Therefore $x = \frac{10500}{0.28}\ = 37500  \mathrm{(D)}$. Ankitamc (talk) 13:32, 17 January 2021 (EST)AnkitAmc. ~edited by mobius247

See also

2007 AMC 12A (ProblemsAnswer KeyResources)
Preceded by
Problem 4
Followed by
Problem 6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 12 Problems and Solutions
2007 AMC 10A (ProblemsAnswer KeyResources)
Preceded by
Problem 6
Followed by
Problem 8
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 10 Problems and Solutions

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