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.

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) (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 ?
--------------
Equations:
Quantity Eq.::: x + y + z = 900,000 dollars
Interest Eq.:::0.10x + 0.08y +0.09z = 133000
Quantity Eq.:::y = 4x
---------------------------------
Substitute 4x for y:
x + 4x + z = 900,000
0.10x + 0.08(4x) + 0.09z = 133000
-----------------------------------------
Simplify:
5x + z = 900,000
0.42x+0.09z = 133000
----
Multiply thru the 1st Eq. by 42.
Multiply thru the 2nd Eq. by 500
-----
210x + 42z = 42*900,000
210x + 45z = 500*133000
----------------------------------
Comment: Those equation conditions result
in negative variable values.
Please check the wording of your problem.
Cheers,
Stan H.
RELATED QUESTIONS
a small corporation borrowed $500,000 to expand its product line. Some of the money was... (answered by josmiceli)

A small corporation borrowed $900,000 to expand its line of toys. Some of the money was... (answered by stanbon)

A SMALL CORPORATION BORROWED $800,000 TO EXPAND ITS LINE OF TOYS. SOME OF THE MONEY WAS... (answered by Fombitz)

A corporation borrowed $760,000 to expand its line of clothing. Some of the money was... (answered by richwmiller)

A clothing company borrows $775,000. Some of the money is borrowed at 8%, some at 9%, and (answered by mananth)

I have been "racking" my brain and wasting a lot of scratch paper over this one. I... (answered by stanbon)

A natural history museum borrows $2,000,000 at simple annual interest to purchase new... (answered by CPhill)

A city zoo borrowed $2,000,000 at simple annual interest to construct a breeding... (answered by addingup)

Sonya borrowed a sum of money and promised to pay 60,000 at the end of one year and 4... (answered by ikleyn)