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A bank has loaned out $500,000, part of it at 6% per annum and the rest of it at 11% per annum.
If the bank receives $43,750 in interest each year, how much was loaned at 6%?
Let x = amt loan out at 6%
The total was given as $500000, therefore
(500000-x) = amt loaned out at 11%
Write these as decimals
6% interest + 11% interest = total interest
.06x + .11(500000-x) = 43750
.06x + 55000 - .11x = 43750
.06x - .11x = 43750 - 55000
-.05x = -11250
x = $225,000 loaned out 6%
You can confirm this by finding the amt loaned 11% (subtract 225000 from 500000)
then finding the interest earned on the this, add to the above interest and confirm it total 43750