Hello, cuteisa89!

I'll set up for you . . .

Using Gaussian elimination, solve the following problem.

A small corporation borrowed $500,000 to expand its product line.

Some of the money was borrowed at 9%, some at 10%, and some at 12%.

How much was borrowed at each rate if the annual interest was $52,000

and the amount borrowed at 10% was 2.5 times the amount borrowed at 9%?

Let: .

The total borrowed is $500,000: . .(a)

The interest on dollars at 9% is: dollars.

The interest on dollars at 10% is: dollars.

The interest on dollars at 12% is: dollars.

. . The total interest was $52,000: .

Multiply by 100: . .(b)

The amount borrowed at 10% was 2.5 times the amount borrowed at 9%:

. .

Multiply by 2: . .(c)

And we have the sytem: .

Now solve it . . .