2007 AMC 12A Problem 5

Question

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?

30{,}000

32{,}500

35{,}000

37{,}500

40{,}000

After the

20\%

federal tax,

80\%

remains; the state tax is

10\%

of that

The two taxes together are

20\%+8\%=28\%

of the inheritance

After federal taxes, Mr. Public keeps

80\%

of his inheritance.

He pays

10\%

of that in state taxes, which is

8\%

of the inheritance.

His total tax is

20\%+8\%=28\%

of the inheritance, so the inheritance is

\frac{\$10{,}500}{0.28}=\$37{,}500.

Thus, the correct answer is D.

Problem 5 in other years