Gonzalez Manufacturing borrowed $. Part of the money was borrowed at %, part at %, and part at %. The annual interest was $, and the total amount borrowed at % and % was twice the amount borrowed at %. Use Gaussian elimination or Gauss-Jordan elimination to find the amount borrowed at each rate.

The answer is "rate 12%, 14%, 16% and value 4000, 10000, and 7000".

Step-by-step explanation:

Let the value is x, y, and z. so,

The value of x amount will be borrowed at 12%

The value of y amount will be borrowed at 14%

The value of z amount will be borrowed at 16%

If the total amount= 21000

If the total interest= 3000

calculating the total interest:

The overall amount borrowing at 12% and 14% was half as much as the amount borrowed at 16%.

by calculating the value we have  3 equations that are:

calculate the matrix by above-given value:

by solving the above matrix we get: