Question 1162159
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Here is a non-algebraic method for solving this kind of "mixture" problem.<br>
The general method is often much faster and easier than the standard algebraic method -- although in this problem the difference in the amount of effort is not significant.<br>
(1) All $5900 invested at 5% would have earned $295 interest; all at 10% would have earned $590 interest.<br>
(2) Determine by whatever means you choose (maybe a number line?) that the actual interest of $460 is 165/295 = 33/59 of the way from $295 to $590.<br>
(3) That means 33/59 of the total was invested at the higher rate.<br>
ANSWER: 33/59 of $5900, or $3300, at 10%; the other $2600 at 5%.<br>
CHECK: .10(3300)+.05(2600) = 330+130 = 460<br>