SOLUTION: A museum borrows $2,000,000 at simple annual interest to purchase new exhibits. Let x represent the amount borrowed at 7%, y represent the amount borrowed at 8.5%, and z represe

Question 1107951: A museum borrows $2,000,000 at simple annual interest to purchase new
exhibits. Let x represent the amount borrowed at 7%, y represent the amount borrowed at 8.5%, and z represent the amount borrowed at 9.5%. Set up a system of linear equations to determine how much is borrowed at each rate given that the total annual interest is $169,750 and the amount borrowed at 8.5% is four times the amount borrowed at 9.5%.
Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
Let the amount borrowed at 9.5% be x. Now we have:
at 9.5% = x
at 8.5% = 4x
at 7% = 2,000,000 - 5x
0.095x + 0.085(4x) + 0.07(2,000,000-5x) = 169,750
0.095x + 0.34x + 140,000 - 0.35x = 169,750
0.085x = 29,750
x = 350,000
So the museum borrowed:
At 9.5% = 350K
At 8.5% = 350*4 = 1,400,000
At 7% = 2,000,000 - 5(350,000) = 250,000
--------------------------------
Total borrowed
350,000 + 1,400,000 + 250,000 = 2,000,000 Correct
--------------------------------------
Interest paid:
0.095(350,000) + 0.085(1,400,000) + 0.07(250,000) = 169,750 Correct
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