SOLUTION: A corporation borrows $900,000 to expand its line of clothing. Some of the money is borrowed at 10%, some at 8% and at 9%. The annual interest payment to the lenders is $133,000.

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Question 355110: A corporation borrows $900,000 to expand its line of clothing. Some of the money is borrowed at 10%, some at 8% and at 9%. The annual interest payment to the lenders is $133,000. The amount borrowed at 8% is four times the amount borrowed at 10% . How much is borrowed at each rate ?

Can someone please help me solve this problem ?
Thank you so much.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A corporation borrows $900,000 to expand its line of clothing. Some of the money is borrowed at 10%, some at 8% and at 9%. The annual interest payment to the lenders is $133,000. The amount borrowed at 8% is four times the amount borrowed at 10% . How much is borrowed at each rate ?
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Equations:
Quantity Eq.::: x + y + z = 900,000 dollars
Interest Eq.:::0.10x + 0.08y +0.09z = 133000
Quantity Eq.:::y = 4x
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Substitute 4x for y:
x + 4x + z = 900,000
0.10x + 0.08(4x) + 0.09z = 133000
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Simplify:
5x + z = 900,000
0.42x+0.09z = 133000
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Multiply thru the 1st Eq. by 42.
Multiply thru the 2nd Eq. by 500
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210x + 42z = 42*900,000
210x + 45z = 500*133000
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Comment: Those equation conditions result
in negative variable values.
Please check the wording of your problem.
Cheers,
Stan H.