Question

A bank loaned out $17,500, part of it at the rate of 10% annual interest, and the rest at 14% annual interest. The total interest earned for both loans was $2,170.00. How much was loaned at each rate?

$ ______was loaned at 10% and
$______ was loaned at 14%.

Answer 1

$7 000 was loaned at 10 % and

$10 500 was loaned at 14 %

Explanation:

Let x = amount loaned at 10 %

Then 17 500 - x = amount loaned at 14 %

0.10x = interest on 10 % loan

0.14(17 500 - x) = interest on 14 % loan

2170.00 = total interest

`\begin{array}{rcl}0.10x + 0.14(17 500 - x) & = & 2170.00\\0.10x + 2450 - 0.14x & = & 2170.00\\2450 - 0.04x & = & 2170.00\\-0.04x & = & -280\\\\x & = & (-280)/(-0.04)\\\\x & = & \mathbf{7000}\\\\\end{array}`

$7000 was loaned at 10 % and

$10 500 was loaned at 14 %

Check:

\
`\begin{array}{rcl}0.10* 7000 + 0.14(17 500 - 7000) & = & 2170\\700 + 0.14(10 500) & = & 2170\\700 + 1470 & = & 2170\\2170 & = & 2170\\\end{array}`

OK.