Difference between revisions of "2001 AMC 12 Problems/Problem 3"
(→Solution 2) |
(→Solution 2) |
||
Line 37: | Line 37: | ||
We are also given that <cmath>T = (p + 0.25)\%\cdot A = p\%\cot A + 0.25\%\cdot A</cmath> | We are also given that <cmath>T = (p + 0.25)\%\cdot A = p\%\cot 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> | + | Solve for <math>A</math> to obtain <math>A = 32000</math>. <math>\boxed{B}</math> |
== See Also == | == See Also == |
Revision as of 18:06, 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.
Contents
[hide]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 .
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.