A small software corporation borrowed 455000 to expand its s

A small software corporation borrowed $455,000 to expand its software line. The corporation borrowed some of the money at 9%, some at 10%, and some at 12%. Use a system of equations to determine how much was borrowed at each rate if the annual interest was $45,800 and the amount borrowed at 10% was 2.5 times the amount borrowed at 9%. Solve the system using matrices.

Amount borrowed at 9% = ?

Amount borrowed at 10% = ?

Amount borrowed at 12% = ?

Solution

Let x be the amount borrowed at 10% and let y be the amount borrowed at 9%.
We know the amount borrowed at 12% is 45000(x+y) .
10% is 2.5 times the amount borrowed at 9% we have that 2.5y=x.
so
1.12(455000-3.5y)+1.1(2.5y)+1.09-455000 = 45800

x+y+z=455000 ,0.09x+0.10y+0.12z=45800 , y=2.5x
solve these three equation
and we know y=2.5x
so the value we get is
x = 110000
y = 275000
z = 70000
Answer