Difference between revisions of "1996 AJHSME Problems/Problem 18"
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==Problem== | ==Problem== | ||
| − | Ana's monthly salary was < | + | Ana's monthly salary was <math>\$2000</math> in May. In June she received a 20% raise. In July she received a 20% pay cut. After the two changes in June and July, Ana's monthly salary was |
<math>\text{(A)}\ 1920\text{ dollars} \qquad \text{(B)}\ 1980\text{ dollars} \qquad \text{(C)}\ 2000\text{ dollars} \qquad \text{(D)}\ 2020\text{ dollars} \qquad \text{(E)}\ 2040\text{ dollars}</math> | <math>\text{(A)}\ 1920\text{ dollars} \qquad \text{(B)}\ 1980\text{ dollars} \qquad \text{(C)}\ 2000\text{ dollars} \qquad \text{(D)}\ 2020\text{ dollars} \qquad \text{(E)}\ 2040\text{ dollars}</math> | ||
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==Solution== | ==Solution== | ||
| − | + | Notice that a 20% raise translates to Ana's monthly salary multiplied by <math>(100 + 10)\% = 120\%</math>, and a 20% pay cut translates to her salary multiplied by <math>100\% - 20\% = 80\%</math>, so | |
| − | + | ||
| + | <cmath>2000 \cdot 120\% = 2400</cmath> | ||
| + | <cmath>2400 \cdot 80\% = 1920 \rightarrow \boxed{\textbf{A}}</cmath> | ||
| + | |||
| + | ~SpeedCuber7 | ||
==See Also== | ==See Also== | ||
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* [[AJHSME Problems and Solutions]] | * [[AJHSME Problems and Solutions]] | ||
* [[Mathematics competition resources]] | * [[Mathematics competition resources]] | ||
| + | {{MAA Notice}} | ||
Latest revision as of 04:49, 27 July 2024
Problem
Ana's monthly salary was 
in May. In June she received a 20% raise. In July she received a 20% pay cut. After the two changes in June and July, Ana's monthly salary was
Solution
Notice that a 20% raise translates to Ana's monthly salary multiplied by 
, and a 20% pay cut translates to her salary multiplied by 
, so
![\[2000 \cdot 120\% = 2400\]](http://latex.artofproblemsolving.com/2/c/8/2c8374e5fa552835f77f8fe18666b04941ac82b8.png)
![\[2400 \cdot 80\% = 1920 \rightarrow \boxed{\textbf{A}}\]](http://latex.artofproblemsolving.com/b/3/8/b38b8e24822b0d509418188e27f09e13cee65d76.png)
~SpeedCuber7
See Also
| 1996 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 17 |
Followed by Problem 19 | |
| 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 AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
