2001 AMC 12 Problems/Problem 3: Difference between revisions
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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 | ||
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