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Difference between revisions of "1996 AJHSME Problems/Problem 18"
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==Problem==
 
==Problem==
  
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Ana's monthly salary was <dollar/>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
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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==
  
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In June, Ana's pay is <math>2000 \cdot 1.2 = 2400</math>
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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
  
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In July, Ana's pay is <math>2400 \cdot 0.8 = 1920</math>, giving an answer of <math>\boxed{A}</math>
+
 
 +
<cmath>2000 \cdot 120\% = 2400</cmath>
 +
<cmath>2400 \cdot 80\% = 1920 \rightarrow \boxed{\textbf{A}}</cmath>
 +
 
 +
~SpeedCuber7
  
 
==See Also==
 
==See Also==

Latest revision as of 04:49, 27 July 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 $(100 + 10)\% = 120\%$, 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 (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

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