Question 1136030
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Here is a completely different method without algebra which, if you understand how to use it, can get you to the answer to a problem like this much faster and with far less effort than traditional algebraic methods.<br>
This is essentially a mixture problem -- you are mixing investments at 5% and 7% and receiving an overall percentage return somewhere between 5% and 7%.<br>
The key to this method of solving mixture problems is that the ratio in which the total investment is split exactly determines where the overall percentage lies between the 5% and 7%.<br>
$43,000 all at 5% would yield $2150 interest.
$43,000 all at 7% would yield $3010 interest.<br>
Find where the actual interest of $2430 lies between $2150 and $3010:<br>
3010-2150 = 860; 2430-2150 = 280; 280/860 = 28/86 = 14/43<br>
Those simple calculations show that $2430 is 14/43 of the way from $2150 to $3010; that means 14/43 of the total investment was at the higher rate.<br>
ANSWER: 14/43 of $43,000, or $14,000, at 7%; the rest, $29,000, at 5%.<br>
CHECK: .07(14000)+.05(29000) = 980+1450 = 1430