2007 AMC 10A Problem 7

Problem 7 of 25EasierAlgebra

Last year Mr. John 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

\$10{,}500

for both taxes. How many dollars was the inheritance?

Show solution

Solution

After federal taxes, Mr. Public keeps

80\%

of his inheritance. State taxes take

10\%

of that, which is

8\%

of the inheritance. The total tax is

20\% + 8\% = 28\%

of the inheritance, so the inheritance is

\dfrac{10{,}500}{0.28} = 37{,}500.

Thus, the correct answer is D.