how to solve it?

Question

A bank loaned out $36,500, part of it at the rate of 10% annual interest, and the rest at 8% annual interest. The total interest earned for both loans was $3,290.00. How much was loaned at each rate?

Answer 1

3290/36500 = slightly more than 9%

so slightly more than half will be at 10%, slightly less than half at 8%

half is $18250

.10x + .08(36500 -x) = 3290

.02x = 3290 - .08(36500) = 3290 - 2920 = 370

x = 370/.02 = 185/.01 = $18500 at 10%

$18,000 at 8%