Question 534061: A clothing company borrows $775,000. Some of the money is borrowed at 8%, some at 9%, and some at 10% simple annual interest. How much is borrowed at each rate if the total annual interest is $67,500 and the amount borrowed at 8% is four times the amount borrowed at 10%?
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! 8%--------------------x
9%--------------------y
10%-------------------z
x=4z
therefore 8% -----------4z
4z+y+z=775000
5z+y=775000...................(1)
0.08*4z+0.09y+0.1z=67500
0.32z+0.09y+0.1z=67500
0.42z+0.09y=67500.............(2)
5 z + 1 y = 775000 .............1
0.42 z + 0.09 y = 67500 .............2
Eliminate y
multiply (1)by -0.09
Multiply (2) by 1
-0.45 z -0.09 y = -69750
0.42 z 0.09 y = 67500
Add the two equations
-0.03 z = -2250
/ -0.03
z = 75,000.00
plug value of z in (1)
5 z + 1 y = 775000
375000 + 1 y = 775000
1 y = 775000 -375000
1 y = 400000
y = 400000.00
10% ------------$75000
9%--------------$400000
8%--------------4*75000= $300000
CHECK
75000*0.1+400000*0.09+300000*0.08=67500
m.ananth@hotmail.ca
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