Question 1042237: A city zoo borrowed $2,000,000 at simple annual interest to construct a breeding facility. Some of the money was borrowed at 7%, some at 8%, and some at 11%. Use a system of linear equations to determine how much was borrowed at each rate given that the total annual interest was $164,500 and the amount borrowed at 7% was twice the amount borrowed at 11%. Solve the system of linear equations using matrices.
Answer by addingup(3677)   (Show Source):
You can put this solution on YOUR website! 2,000,000 was borrowed:
0.07x+0.11(1/2x)
+
0.08(2,000,000-(x+1/2x)
= 164,500
:
(0.07+0.055)x+0.08(2,000,000-1 1/2x) = 164,500
0.125x+160000-0.12x = 164,500
0.005x = 4,500 = 900,000 is the amount borrowed at 7%
1/2*900,000 = 450,000 is the amount borrowed at 11%
2,000,000-1,350,000 = 650,000 is the amount borrowed at 8%
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Check:
900,000*.07 = 63,000
450,000*.11 = 49,500
650,000*.08 = 52,000
Total. . . . 164,500 Correct
:
John
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