Difference between revisions of "2001 AMC 12 Problems/Problem 3"
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&= p\%\cdot A + 2\%\cdot(A - 28000) | &= p\%\cdot A + 2\%\cdot(A - 28000) | ||
\end{align*}</cmath> | \end{align*}</cmath> | ||
− | We are also given that <cmath>T = (p + 0.25)\%\cdot A = p\%\ | + | We are also given that <cmath>T = (p + 0.25)\%\cdot A = p\%\cdot A + 0.25\%\cdot A</cmath> |
Thus, <cmath>p\%\cdot A + 2\%\cdot(A - 28000) = p\%\cot A + 0.25\%\cdot A</cmath> <cmath>2\%\cdot(A - 28000) = 0.25\%\cdot A</cmath> | Thus, <cmath>p\%\cdot A + 2\%\cdot(A - 28000) = p\%\cot A + 0.25\%\cdot A</cmath> <cmath>2\%\cdot(A - 28000) = 0.25\%\cdot A</cmath> | ||
Solve for <math>A</math> to obtain <math>A = 32000</math>. <math>\boxed{B}</math> | Solve for <math>A</math> to obtain <math>A = 32000</math>. <math>\boxed{B}</math> |
Revision as of 19:07, 30 June 2019
- The following problem is from both the 2001 AMC 12 #3 and 2001 AMC 10 #9, so both problems redirect to this page.
Problem
The state income tax where Kristin lives is levied at the rate of of the first of annual income plus of any amount above . Kristin noticed that the state income tax she paid amounted to of her annual income. What was her annual income?
Solution
Solution 1
Let the income amount be denoted by .
We know that .
We can now try to solve for :
So the answer is
Solution 2
Let , be Kristin's annual income and the income tax total, respectively. Notice that We are also given that Thus, Solve for to obtain .
~ Nafer
See Also
2001 AMC 12 (Problems • Answer Key • Resources) | |
Preceded by Problem 2 |
Followed by Problem 4 |
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 |
2001 AMC 10 (Problems • Answer Key • Resources) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
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.