Question 1120418
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See if you understand this alternative to the traditional algebraic method for solving mixture problems like this.  If you understand it, you will solve this kind of problem much faster and with much less effort than with algebra.<br>
The total of $5400 all invested at 10% would yield $540 interest; all invested at 8% would yield $432 interest.<br>
Where the actual interest of $492 lies between those two numbers determines the ratio in which the money must be split between the two investments.<br>
I will first show just the required calculations, to show how fast and easy the method is.  Then I will explain the method.<br>
540-432 = 108
492-432 = 60
60/108 = 5/9<br>
Answer: 5/9 of the money should be invested at the higher rate.<br>
5/9 of $5400 = 5*$600 = $3000 at 10%; the other 4/9 = $2400 at 8%.<br>
Quick explanation....<br>
Think of the three numbers on a number line -- the amount of interest if all at 8%, the actual amount of interest, and the amount of interest if all at 10%: 432, 492, and 540.<br>
The three quick calculations shown above show that the actual number, 492, is 5/9 of the way from the lower number, 432, to the higher number, 540.<br>
That means 5/9 of the money must be invested at the higher rate.