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Difference between revisions of "1953 AHSME Problems/Problem 17"

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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>.
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==See Also==
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{{AHSME 50p box|year=1953|num-b=16|num-a=18}}
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{{MAA Notice}}

Latest revision as of 00:47, 26 January 2020

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 $\boxed{\textbf{(B)}\ 4.8\%}$.

See Also

1953 AHSC (Problems • Answer Key • Resources)
Preceded by
Problem 16 		Followed by
Problem 18
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 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50
All AHSME Problems and Solutions


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