Difference between revisions of "2007 AMC 12A Problems/Problem 5"
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| + | {{duplicate|[[2007 AMC 12A Problems|2007 AMC 12A #5]] and [[2007 AMC 10A Problems/Problem 7|2007 AMC 10A #7]]}} | ||
==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 for both taxes. How many dollars was his inheritance? | 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>(\mathrm {A})\ 30000 \qquad (\mathrm {B})\ 32500 \qquad(\mathrm {C})\ 35000 \qquad(\mathrm {D})\ 37500 \qquad(\mathrm {E})\ 40000</math> |
==Solution== | ==Solution== | ||
| − | After paying his taxes, he has <math>.8*.9=.72</math> of the inheritance left. Since 10500 is .28 of the inheritance, the whole inheritance is <math>\frac{10500}{0.28}=37500\ \mathrm{(D)}</math>. | + | After paying his taxes, he has <math>0.8*0.9=0.72</math> of the inheritance left. Since <math>10500</math> is <math>0.28</math> of the inheritance, the whole inheritance is <math>\frac{10500}{0.28}=37500\ \mathrm{(D)}</math>. |
==See also== | ==See also== | ||
{{AMC12 box|year=2007|ab=A|num-b=4|num-a=6}} | {{AMC12 box|year=2007|ab=A|num-b=4|num-a=6}} | ||
| + | {{AMC10 box|year=2007|ab=A|num-b=6|num-a=8}} | ||
[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
Revision as of 15:07, 6 January 2008
- The following problem is from both the 2007 AMC 12A #5 and 2007 AMC 10A #7, so both problems redirect to this page.
Problem
Last year Mr. Jon Q. Public received an inheritance. He paid 
in federal taxes on the inheritance, and paid 
of what he had left in state taxes. He paid a total of 
10500 for both taxes. How many dollars was his inheritance?
Solution
After paying his taxes, he has 
of the inheritance left. Since 
is 
of the inheritance, the whole inheritance is 
.
See also
| 2007 AMC 12A (Problems • Answer Key • Resources) | |
| 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 | |
| 2007 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 6 |
Followed by Problem 8 | |
| 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 10 Problems and Solutions | ||
