Difference between revisions of "1953 AHSME Problems/Problem 17"
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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 $ invested at
% and the rest at
%. If his annual return on each investment is the same, the average rate of interest which he realizes of the $4500 is:
Solution
You are trying to find , where
is the principle for one investment. To find
, solve
.
will come out to be
. Then, plug in x into the first equation,
, to get
. Finally, convert that to a percentage and you get
.