2007 AMC 12A Problems/Problem 5

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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 $$$10500 for both taxes. How many dollars was his inheritance?$(\mathrm {A})30000$$ (Error compiling LaTeX. Unknown error_msg)(\mathrm {B})32500$$ (Error compiling LaTeX. Unknown error_msg)(\mathrm {C})35000$$ (Error compiling LaTeX. Unknown error_msg)(\mathrm {D})37500$$ (Error compiling LaTeX. Unknown error_msg)(\mathrm {E})40000$

Solution

After paying his taxes, he has $.8*.9=.72$ of the inheritance left. Since 10500 is .28 of the inheritance, the whole inheritance is $\frac{10500}{0.28}=37500\  \mathrm{(D)}$.

See also

2007 AMC 12A (ProblemsAnswer KeyResources)
Preceded by
Problem 4
Followed by
Problem 6
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All AMC 12 Problems and Solutions