Difference between revisions of "2007 AMC 12A Problems/Problem 5"

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==Problem==
 
==Problem==
Last year Mr. Jon Q. Public received an inheritance. He paid <math>20\%</math> in federal taxes on the inheritance, and paid <math>10\%</math> of what he had left in state taxes. He paid a total of <math>\</math>10500<math> for both taxes. How many dollars was his inheritance?
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Last year Mr. Jon Q. Public received an inheritance. He paid <math>20\%</math> in federal taxes on the inheritance, and paid <math>10\%</math> of what he had left in state taxes. He paid a total of <math>\</math>10500 for both taxes. How many dollars was his inheritance?
  
</math>(\mathrm {A})30000<math>  </math>(\mathrm {B})32500<math>  </math>(\mathrm {C})35000<math>  </math>(\mathrm {D})37500<math>  </math>(\mathrm {E})40000$
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<math>(\mathrm {A})30000</math>  <math>(\mathrm {B})32500</math>  <math>(\mathrm {C})35000</math>  <math>(\mathrm {D})37500</math>  <math>(\mathrm {E})40000</math>
  
 
==Solution==
 
==Solution==

Revision as of 19:48, 28 September 2007

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?

$(\mathrm {A})30000$ $(\mathrm {B})32500$ $(\mathrm {C})35000$ $(\mathrm {D})37500$ $(\mathrm {E})40000$

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
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