Difference between revisions of "2001 AMC 12 Problems/Problem 3"
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Revision as of 20:02, 3 July 2013
- 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 $p%$ (Error compiling LaTeX. Unknown error_msg) of the first
<dollar/>
of annual income plus $(p + 2)%$ (Error compiling LaTeX. Unknown error_msg) of any amount above <dollar/>. Kristin
noticed that the state income tax she paid amounted to $(p + 0.25)%$ (Error compiling LaTeX. Unknown error_msg) of her
annual income. What was her annual income?
<dollar/>
<dollar/>
<dollar/>
<dollar/>
<dollar/>
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. 
