Difference between revisions of "1996 AJHSME Problems/Problem 18"

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==Problem==
 
==Problem==
  
Ana's monthly salary was <math>$2000</math> in May.  In June she received a 10% raise.  In July she received a 20% pay cut.  After the two changes in June and July, Ana's monthly salary was
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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==
  
2000 times (1+20%) times (1-20%) equals to <math>1920</math>.
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Notice that a 20% raise translates to Ana's monthly salary multiplied by <math>(100 + 20)\% = 120\%</math>, and a 20% pay cut translates to her salary multiplied by <math>100\% - 20\% = 80\%</math>, so
  
The answer is <math>\boxed{A}</math>
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<cmath>2000 \cdot 120\% = 2400</cmath>
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<cmath>2400 \cdot 80\% = 1920 \rightarrow \boxed{\textbf{A}}</cmath>
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~SpeedCuber7
  
 
==See Also==
 
==See Also==

Latest revision as of 13:23, 10 December 2024

Problem

Ana's monthly salary was $$2000$ 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

$\text{(A)}\ 1920\text{ dollars} \qquad \text{(B)}\ 1980\text{ dollars} \qquad \text{(C)}\ 2000\text{ dollars} \qquad \text{(D)}\ 2020\text{ dollars} \qquad \text{(E)}\ 2040\text{ dollars}$

Solution

Notice that a 20% raise translates to Ana's monthly salary multiplied by $(100 + 20)\% = 120\%$, and a 20% pay cut translates to her salary multiplied by $100\% - 20\% = 80\%$, so


\[2000 \cdot 120\% = 2400\] \[2400 \cdot 80\% = 1920 \rightarrow \boxed{\textbf{A}}\]

~SpeedCuber7

See Also

1996 AJHSME (ProblemsAnswer KeyResources)
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

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