Gonzalez Manufacturing borrowed $21000. Part of the money was borrowed at 10%, part at 12%, and part at 14%. The total amount borrowed at 10% and 12%
was twice the amount borrowed at 14%. Find the amount borrowed at each rate if the annual interest was $2580
How much money was borrowed at 10%?
How much money was borrowed at 12%?
How much money was borrowed at 14%?

You want to know the amount borrowed at 10%, 12%, and 14% if the total borrowed was $21000, the total interest was $2580, and the total of amounts borrowed at 10% and 14% was double the amount borrowed at 12%.

Equations

The relations give rise to three equations. If we let x, y, z represent the respective amounts borrowed at 10%, 12%, and 14%, we have ...

x + y + z = 21000 . . . . . . total borrowed

0.10x +0.12y +0.14z = 2580 . . . . . . total interest

x + y = 2z . . . . . . . . . . . relationship between amounts

Writing the last equation as ...

x -2y +z = 0

we can formulate the problem as a matrix equation and use a solver to find the solution. We have done that in the attachment. It tells us the amounts borrowed are ...

10% — $5500
12% — $7000
14% — $8500

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Additional comment

Recognizing that the amount at 12% is 1/3 of the total, we can use that fact to rewrite the other two equations. The interest on the $7000 at 12% is $840, so we have ...

x + y = 14000
0.10x +0.14y = 1740

These two equations have the solution shown above. (It is usually convenient to solve them by substituting for x in the second equation.)

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