2007 AMC 12A Problem 5

Below is the professionally curated solution for Problem 5 of the 2007 AMC 12A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2007 AMC 12A solutions, or check the answer key.

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Concepts:percentage work backwards

Difficulty rating: 1200

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?

$30{,}000$

$32{,}500$

$35{,}000$

$37{,}500$

$40{,}000$

Solution:

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

Thus, the correct answer is D.

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