Difference between revisions of "1985 AJHSME Problems/Problem 21"

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==Solution==
 
==Solution==
  
Assume his salary is 100 dollars then the next year he would have 110 dollars then the next year he would have 121 dollars then the next year he would have 133.1 dollars then, the last year, he would have 146.41; therefore the answer is <math>\boxed{\text{E}}</math>.
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Assume his salary is <math>100</math> dollars. Then in the next year, he would have <math>110 dollars</math>, and in the next he would have <math>121</math> dollars. The next year he would have <math>133.1</math> dollars and in the last year, he would have <math>146.41</math>. As the total increase is greater than <math>45%</math>, the answer is <math>\boxed{\text{E}}</math>.
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Note that we could have generalized this for any integer <math>n</math>.
  
 
==See Also==
 
==See Also==

Revision as of 15:42, 26 November 2016

Problem

Mr. Green receives a $10\%$ raise every year. His salary after four such raises has gone up by what percent?

$\text{(A)}\ \text{less than }40\% \qquad \text{(B)}\ 40\% \qquad \text{(C)}\ 44\% \qquad \text{(D)}\ 45\% \qquad \text{(E)}\ \text{more than }45\%$

Solution

Assume his salary is $100$ dollars. Then in the next year, he would have $110 dollars$, and in the next he would have $121$ dollars. The next year he would have $133.1$ dollars and in the last year, he would have $146.41$. As the total increase is greater than $45%$ (Error compiling LaTeX. ! Missing $ inserted.), the answer is $\boxed{\text{E}}$.

Note that we could have generalized this for any integer $n$.

See Also

1985 AJHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 20
Followed by
Problem 22
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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