2007 AMC 12A Problems/Problem 5

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 ==> 0.28x = 10500. Therefore x = $\frac{10500}{.28}\ = 37500 \mathrm{(D)}$. Ankitamc (talk) 13:32, 17 January 2021 (EST)AnkitAmc.

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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