Question 1183978
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The other tutor showed a good formal algebraic solution using the standard method.<br>
If a formal algebraic solution is not required, and if the speed of getting an answer is important (as in a timed math competition), then here is a very fast and easy way to solve this problem (and many similar problems) mentally.<br>
(1) $10000 all invested at 4% would yield $400 interest; all at 6% would yield $600 interest.
(2) The actual interest $560 is 4/5 of the way from $400 to $600.  (Picturing the three numbers 400, 560, and 600 on a number line might help: 400 to 600 is a difference of 200; 400 to 560 is a difference of 160; 160/200 = 4/5.)
(3) That means 4/5 of the $10000 was invested at the higher rate.<br>
ANSWER: 4/5 of $10000, or $8000, was invested at 6%; the other $2000 at 4%.<br>
CHECK: .06(8000)+.04(2000) = 480+80 = 560<br>