a small software corp question

Question

A small software corporation borrowed $195,000 to expand its software line. The corporation borrowed some of the money at 3%, some at 4%, and some at 5%. Use a system of equations to determine how much was borrowed at each rate when the annual interest was $7,500 and the amount borrowed at 4% was 2 1/2

 times the amount borrowed at 3%. Solve the system using matrices.

amount borrowed at 3%

$

amount borrowed at 4%

$

amount borrowed at 5%

$

Answer 1

Let a be the amountbborrowedcat 3%.

Let be be that amount borrowed at 4%.

Let c be the amount borrowed at 5%.

0.03 * a + .04 * b + 0.5 * c = 7500

b = 2.5 * a

a + b + c = 195000

In matrix notation:

| 0.03 0.04 0.05 | | a | | 7500. |

| 2.5 -1.0 0.0 | | b | = | 0.0. |

| 1.0. 1.0 1.0 | | c | | 195000 |

a = $50,000

b = $125,000

c = $20,000

Checked to verify that the equations are all satisfied.