Difference between revisions of "2001 AMC 12 Problems/Problem 3"
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== Problem == | == Problem == | ||
− | The state income tax where Kristin lives is levied at the rate of <math>p%</math> of the first | + | The state income tax where Kristin lives is levied at the rate of <math>p\%</math> of the first |
− | + | <math>\textdollar 28000</math> of annual income plus <math>(p + 2)\%</math> of any amount above <math>\textdollar 28000</math>. Kristin | |
− | noticed that the state income tax she paid amounted to <math>(p + 0.25)%</math> of her | + | noticed that the state income tax she paid amounted to <math>(p + 0.25)\%</math> of her |
− | annual income. What was her annual income? | + | annual income. What was her annual income? |
− | <math>\text{(A)}\, | + | <math>\text{(A)}\,\textdollar 28000 \qquad \text{(B)}\,\textdollar 32000 \qquad \text{(C)}\,\textdollar 35000 \qquad \text{(D)}\,\textdollar 42000 \qquad \text{(E)}\,\textdollar 56000</math> |
== Solution== | == Solution== |
Revision as of 19:35, 13 June 2015
- 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
Let the income amount be denoted by .
We know that .
We can now try to solve for :
So the answer is
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.