Difference between revisions of "2007 AMC 12A Problems/Problem 5"
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<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
[hide]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.