Question 1149612
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By the standard algebraic solution method....<br>
Let x be the amount at 5%; then the amount at 7% is 27000-x.  Then the total interest is 1570 dollars:<br>
{{{.05(x)+.07(27000-x) = 1570}}}
{{{.05x+1890-.07x = 1570}}}
...<br>
You can finish the solution by that method.<br>
Here is a non-algebraic method for finding the answer to "mixture" problems like this that I find much easier and faster than that algebraic approach.<br>
(1a) $27000 all at 5% would yield $1350 interest
(1b) the actual interest was $1570
(1c) $27000 all at 7% would yield $1890 interest<br>
(2) The actual interest of $1570 is 220/540 = 11/27 of the way from $1350 to $1890.  (If it helps, picture the three interest amounts on a number line.  $1350 to $1570 is a difference of $220; $1350 to $1890 is a difference of $540.  So $1570 is 220/540 of the way from $1350 to $1890.)<br>
That means 11/27 of the investment was at the higher rate.<br>
ANSWER: 11/27 of $27,000, or $11,000, at 7%; the other $16,000 at 5%.<br>
CHECK: .07(11000)+.05(16000) = 770+800 = 1570<br>