Question 1148298
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Using the traditional algebraic solution method....<br>
8% of x, plus 5% of ($10,000-x), equals $575:<br>
{{{.08(x)+.05(10000-x) = 575}}}
{{{.08x+500-.05x = 575}}}
{{{.03x = 75}}}
{{{x = 75/.03 = 2500}}}<br>
ANSWER: $2500 at 8%; the other $7500 at 5%.<br>
Here is a non-algebraic method that will get you to the solution to "mixture" problems like this much faster and with far less work, if you understand how to use it.<br>
(1) The $10,000 all earning 8% interest would yield $800 interest; all at 5% would yield $500 interest.
(2) The actual interest, $575, is 1/4 of the way from $500 to $800.  (Picture the three numbers on a number line -- 500, 575, and 800; 575 is 1/4 of the way from 500 to 800.)
(3) That means 1/4 of the total was invested at the higher rate.<br>
ANSWER: 1/4 of $10,000, or $2500, at 8%; the other $7500 at 5%.<br>