Question

A city zoo borrowed $2,000,000 at simple annual interest to construct a breeding facility. some of the money was borrowed at 6%, some at 7%, and some at 10%. use a system of linear equations to determine how much was borrowed at each rate given that the total annual interest was $145,500 and the amount borrowed at 6% was twice the amount borrowed at 10%. solve the system of linear equations using matrices.

Answer 1

given:
amount borrowed= $2,000,000.
rate of interests are 6%,7% and 10 % respectively
0.06x+0.10(1/2x)+0.07(2,000,000-(x+0.5x)= 145,500
:
(0.06+0.05)x+0.07(2,000,000- 1.5x) = 145,500
0.11x+140000-0.105x = 145,500
0.005x = 5,500
x = 1,100,000 is the amount borrowed at 6%
1/2*1100,000 = 550,000 is the amount borrowed at 10%
2,000,000-1,650,000 = 350,000 is the amount borrowed at 8%