Question 1206863
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The response from the other tutor shows a typical formal algebraic solution.<br>
The discussion below shows a less formal process for solving any 2-part mixture problems like this.<br>
The idea behind this method is that the ratio between the amounts invested in the two accounts is exactly determined by where the overall percentage return lies between the percentages of the two accounts.<br>
$24,000 all invested at 5% would earn $1200 interest; all invested at 7% would earn $1680 interest.<br>
Picture the three interest amounts -- $1200, $1400, and $1680 -- on a number line and observe/calculate that $1400 is (1400-1200)/(1680-1200) = 200/480 = 5/12 of the way from $1200 to $1680.<br>
That means 5/12 of the total was invested at the higher rate.<br>
5/12 of $24,000 is $10,000.  So $10,000 was invested at 7% and the other $14,000 at 5%.<br>
ANSWER: $10,000 at 7%; $14,000 at 5%<br>
CHECK: .07(10000)+.05(14000) = 700+700 = 1400<br>