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

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(Solution)
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==Solution==
 
==Solution==
  
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>.  
+
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>boxedE</math>.  
  
 
Note that we could have generalized this for any integer <math>n</math>.
 
Note that we could have generalized this for any integer <math>n</math>.

Revision as of 15:43, 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 $boxedE$.

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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