Question 1144700
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Traditional algebraic approach....<br>
x amount invested at 7 1/4%, plus (30,000-x) invested at 3%, yields interest of 30,000 at 6.5%:<br>
{{{.0725(x)+.03(30000-x) = .065(30000)}}}<br>
Solve for x....<br>
A very different method for solving "mixture" problems like this....<br>
(1) 6.5% is 14/17 of the way from 3% to 7.25%.  (Look at the three numbers on a number line: 3, 6.5, and 7.25.  The distance from 3 to 7.25 is 4.25; the distance from 3 to 6.5 is 3.5.  3.5/4.25 = 14/17.)<br>
That means 14/17 of the $30,000 total has to be invested at the higher rate to yield 6.5% interest.<br>
ANSWER: at least 14/17 of $30,000, which rounded UP to the next whole cent is $24,705.89.<br>
That method is a quick and easy way to solve mixture problems like this without going through the process of writing and solving an equation.