Question

Gonzalez Manufacturing borrowed $45000. Part of the money was borrowed at 10%, part at 12%, and part at 14%. The annual interest was $5420, and the total amount borrowed at 10% and 12%

was twice the amount borrowed at 14%. Use Gaussian elimination or Gauss-Jordan elimination to find the amount borrowed at each rate.
How much money was borrowed at 10%?

Answer 1

To find the amount borrowed at 10%, we can solve a system of equations based on the given information. The amount borrowed at 10% is $15,000.

Step-by-step explanation:

To solve this problem, we need to set up a system of equations based on the given information.

Let's assume that the amount borrowed at 10% is x, the amount borrowed at 12% is y, and the amount borrowed at 14% is z.

The first equation we can form is:

x + y + z = $45,000 (the total amount borrowed).

The second equation is:

x + y = 2z (the total amount borrowed at 10% and 12% is twice the amount borrowed at 14%).

The third equation is based on the annual interest of

$5,420: 0.10x + 0.12y + 0.14z = $5,420.

Using Gaussian elimination or Gauss-Jordan elimination, we can solve this system of equations to find the values of x, y, and z.

After solving, we find that the amount borrowed at 10% is $15,000.