Question 1144700: A company invests a total of $30,000 of surplus funds at two annual rates of interest: 3% and 7 1/4%. It wishes an annual yield of no less than 6 1/2%. What is the least amount of money that the company must invest at the 7 1/4% rate?
Answer by greenestamps(13203)   (Show Source):
You can put this solution on YOUR website!
Traditional algebraic approach....
x amount invested at 7 1/4%, plus (30,000-x) invested at 3%, yields interest of 30,000 at 6.5%:
Solve for x....
A very different method for solving "mixture" problems like this....
(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.)
That means 14/17 of the $30,000 total has to be invested at the higher rate to yield 6.5% interest.
ANSWER: at least 14/17 of $30,000, which rounded UP to the next whole cent is $24,705.89.
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.
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