SOLUTION: I have been "racking" my brain and wasting a lot of scratch paper over this one. I just can't seem toA small corporation borrowed $775,000 to expand it's software line. Some of

Question 86184This question is from textbook COLLEGE ALGEBRA, A TEXTBOOK APPROACH
:
I have been "racking" my brain and wasting a lot of scratch paper over this one. I just can't seem toA small corporation borrowed $775,000 to expand it's software line. 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 was $67,000 and the amount borrowed at 8% was four times the amount borrowed at 10%?
visualize the format. Thanks in advance. This question is from textbook COLLEGE ALGEBRA, A TEXTBOOK APPROACH

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A small corporation borrowed $775,000 to expand it's software line. 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 was $67,000 and the amount borrowed at 8% was four times the amount borrowed at 10%?
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Let amt. borrowed at 10% be x; interest on this is 0.10x dollars
Amt. borrowed at 8% is 4x; interest on this is 0.08(4x)=.32x dollars
Amt. borrowed at 9% is "775,000-5x"; interest is 0.09(775,000-5x) = 69750-0.45x
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EQUATION:
interest + interest + interest = 67000
0.10x + .32x +69750-0.45x = 67000
10x + 32x + 6975000 -45x = 6700000
-3x = -275000
x=$91,666.67 (amt. borrowed at 10%)
4x=$366,666.67 (amt. borrowed at 8%
777,000-5x = $316,666.66 (amt. borrowed at 9%)
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Cheers,
Stan H.
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