# Multivariable Linear Systems

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• Apr 28th 2011, 08:29 PM
NeoSonata
Multivariable Linear Systems
[COLOR=rgb(0, 0, 0)]Problem:[/COLOR] A Corporation borrowed \$775,000 to expand. some of the money was borrowed at 8%, some at 9%, and some at 10%. How much was borrowed at each rate if the annual interest owed was \$67,500 and the amount borrowed at 8% was four times the amount borrowed at 10%?

Is my set up correct?

x + y + z = 775,000
.08x + .09y + .10z = 67,500
z= 4x
• Apr 28th 2011, 08:54 PM
TheChaz
Quote:

Originally Posted by NeoSonata
[COLOR=rgb(0, 0, 0)]Problem:[/COLOR] A Corporation borrowed \$775,000 to expand. some of the money was borrowed at 8%, some at 9%, and some at 10%. How much was borrowed at each rate if the annual interest owed was \$67,500 and the amount borrowed at 8% was four times the amount borrowed at 10%?

Is my set up correct?

x + y + z = 775,000
.08x + .09y + .10z = 67,500
z= 4x

Since you picked x to be "the amount borrowed at 8%" (and z to be "the amount borrowed at 10%), the last equation should read x = 4z.