Question

a natural history museum borrowed $2,000,000 at simple annual interest to purchase new exhibits. Some of the money was borowed at 7%, some at 8.5%, and some at 9.5%. Use a system of linear equations to determine how much was borrowed at each rate if the total annual interest was $169,750 and the amount borrowed at 8.5% was four times the amount borrowed at 9.5%. Solve the system of linear equations using matrices.

Answer 1

Solve using matrices ???

What can be easier than the following? :

amount borrowed at 9.5% ---- x
amount borrowed at 8.5% ---- 4x
amount borrowed at 7% = 2,000,000 - 5x

.095x + .085(4x) + .07(2000000-5x) = 169750

solve for x , and sub back in my definitions

Answer 2

x+y+z = 2000000
.07x + .085y + .095z = 169750
y = 4z

see the matrix solution at

http://www.wolframalpha.com/input/?i={{1,1,1},{.07,.085,.095},{0,1,-4}}*{{x},{y},{z}}+%3D+{{2000000},{169750},{0}}

{{1,1,1},{.07,.085,.095},{0,1,-4}}*{{x},{y},{z}} = {{2000000},{169750},{0}}