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1953 AHSME Problems/Problem 17: Difference between revisions

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Problem
==Problem==


A man has part of \$<math>4500</math> invested at <math>4</math>% and the rest at <math>6</math>%. If his annual return on each investment is the same, the average rate of interest which he realizes of the \$4500 is:  
A man has part of \$<math>4500</math> invested at <math>4</math>% and the rest at <math>6</math>%. If his annual return on each investment is the same, the average rate of interest which he realizes of the \$4500 is:  
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Solution
==Solution==


You are trying to find <math>\frac{2(0.06x)}{4500}</math>, where <math>x</math> is the principle for one investment. To find <math>x</math>, solve <math>0.04(4500-x) = 0.06x</math>. <math>X</math> will come out to be <math>1800</math>. Then, plug in x into the first equation, <math>\frac{2(0.06)(1800)}{4500}</math>, to get <math>0.048</math>. Finally, convert that to a percentage and you get <math>\boxed{\textbf{(B)}\ 4.8\%}</math>.
You are trying to find <math>\frac{2(0.06x)}{4500}</math>, where <math>x</math> is the principle for one investment. To find <math>x</math>, solve <math>0.04(4500-x) = 0.06x</math>. <math>X</math> will come out to be <math>1800</math>. Then, plug in x into the first equation, <math>\frac{2(0.06)(1800)}{4500}</math>, to get <math>0.048</math>. Finally, convert that to a percentage and you get <math>\boxed{\textbf{(B)}\ 4.8\%}</math>.

Revision as of 13:31, 23 June 2018

Problem

A man has part of \$$4500$ invested at $4$% and the rest at $6$%. If his annual return on each investment is the same, the average rate of interest which he realizes of the \$4500 is:

$\textbf{(A)}\ 5\% \qquad \textbf{(B)}\ 4.8\% \qquad \textbf{(C)}\ 5.2\% \qquad \textbf{(D)}\ 4.6\% \qquad \textbf{(E)}\ \text{none of these}$


Solution

You are trying to find $\frac{2(0.06x)}{4500}$, where $x$ is the principle for one investment. To find $x$, solve $0.04(4500-x) = 0.06x$. $X$ will come out to be $1800$. Then, plug in x into the first equation, $\frac{2(0.06)(1800)}{4500}$, to get $0.048$. Finally, convert that to a percentage and you get $\boxed{\textbf{(B)}\ 4.8\%}$.

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