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]]}} | {{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> | + | 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>\textdollar10500</math> for both taxes. How many dollars was his inheritance? |
<math>(\mathrm {A})\ 30000 \qquad (\mathrm {B})\ 32500 \qquad(\mathrm {C})\ 35000 \qquad(\mathrm {D})\ 37500 \qquad(\mathrm {E})\ 40000</math> | <math>(\mathrm {A})\ 30000 \qquad (\mathrm {B})\ 32500 \qquad(\mathrm {C})\ 35000 \qquad(\mathrm {D})\ 37500 \qquad(\mathrm {E})\ 40000</math> | ||
| − | ==Solution== | + | ==Solution 1== |
| − | After paying his taxes, he has <math>0.8*0.9=0.72</math> of | + | After paying his taxes, he has <math>0.8*0.9=0.72</math> of his earnings left. Since <math>10500</math> is <math>0.28</math> of his income, he got a total of <math>\frac{10500}{0.28}=37500\ \mathrm{(D)}</math>. |
| + | == Solution 2 == | ||
| + | Let his total inheritance be a number <math>x</math>. The amount of tax he has to pay at first can be represented as <math>0.2x</math>. The amount of money he has left over after this expense can be written as <math>0.8x</math>. He then has to pay <math>10\%</math> tax on this remaining amount, which can be written as <math>0.1(0.8x) = 0.08x</math>. The combined expense of these taxes is <math>10500</math>, so <math>0.2x + 0.08x = 10500 \Longrightarrow 0.28x = 10500</math>. Therefore <math>x = \frac{10500}{0.28}\ = 37500 \mathrm{(D)}</math>. [[User:Ankitamc|Ankitamc]] ([[User talk:Ankitamc|talk]]) 13:32, 17 January 2021 (EST)AnkitAmc. | ||
| + | ~edited by mobius247 | ||
==See also== | ==See also== | ||
Latest revision as of 11:27, 3 June 2021
- The following problem is from both the 2007 AMC 12A #5 and 2007 AMC 10A #7, so both problems redirect to this page.
Contents
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 
for both taxes. How many dollars was his inheritance?
Solution 1
After paying his taxes, he has 
of his earnings left. Since 
is 
of his income, he got a total of 
.
Solution 2
Let his total inheritance be a number 
. The amount of tax he has to pay at first can be represented as 
. The amount of money he has left over after this expense can be written as 
. He then has to pay tax on this remaining amount, which can be written as 
. The combined expense of these taxes is , so 
. Therefore 
. Ankitamc (talk) 13:32, 17 January 2021 (EST)AnkitAmc.
~edited by mobius247
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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
