Question 1149229
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Using the standard formal algebraic solution....<br>
7% of x, plus 9% of (4000-x) equals 300:<br>
{{{.07(x)+.09(4000-x) = 300}}}
{{{7x+9(4000-x) = 30000}}}
{{{7x+36000-9x = 30000}}}
{{{6000 = 2x}}}
{{{x = 3000}}}<br>
ANSWER: $3000 at 7%; $1000 at 9%.<br>
CHECK:
.07(3000)+.09(1000) = 210+90 = 300<br>
Here is a much faster path to solving a mixture problem like this if an algebraic solution is not required.<br>
(1) $4000 all at 7% would yield $280 interest; all at 9% would yield $360 interest.
(2) The actual interest, $300, is 1/4 of the way from $280 to $360.  (Picture the three numbers 280, 300, and 360 on a number line. 280 to 360 is a difference of 80; 280 to 300 is a difference of 20.  20 is 1/4 of 80.)
(3) Therefore, 1/4 of the total was invested at the higher rate.<br>
ANSWER: 1/4 of $4000, or $1000, at 9%; the other $3000 at 7%.<br>
Obviously the same answer as before....<br>