Question

A bank loaned out $31,000, part of it at the rate of 5% annual interest, and the rest at 8% annual interest. The total interest earned for both loans was $2,000.00. How much was loaned at each rate?

$_______ was loaned at 5% and
$_______ was loaned at 8%.

Answer 1

Explanation:

Let x be the amount taken for 5% annual interest.

Let y be the amount taken for 8% annual interest.

x + y = 31000 -------------------(i)

5%of x + 8% of x = 2000

`(5)/(100)x+(8)/(100)y=2000`

0.05x + 0.08y = 2000 -----------------------(ii)

Multiply equation (i) by (-0.05).

(i)*(-0.05) -0.05x - 0.05y = -1550

(ii) 0.05x + 0.08y = 2000 ( Now add & x will be eliminated}

0.03y = 450

y = 450/0.03

y = 15,000

Plugin the value of y in equation (i)

x + 15000 = 31000

x = 31000 - 15000

x = 16000

$ 16,000 was loaned at 5%

$ 15000 was loaned at 8%