SOLUTION: Partners in a business agreed to take out 2 loans totaling $35000. The yearly interest rates were 12% and 15% and the total yearly interest was $4650. Find the amount of each loan

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Partners in a business agreed to take out 2 loans totaling $35000. The yearly interest rates were 12% and 15% and the total yearly interest was $4650. Find the amount of each loan      Log On


   

Question 62082: Partners in a business agreed to take out 2 loans totaling $35000. The yearly interest rates were 12% and 15% and the total yearly interest was $4650. Find the amount of each loan.
Answer by 303795(602) About Me  (Show Source):
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Partners in a business agreed to take out 2 loans totaling $35000. The yearly interest rates were 12% and 15% and the total yearly interest was $4650. Find the amount of each loan.
Let the amount of the loan taken out by the first person be x. The amount taken out by the second person is the rest of the 35000 ie 35000 - x.
The interest paid by the first person must be %2812%2F100%29+%2A+x.
The interest paid by the second person must be %2815%2F100%29+%2A+%2835000+-+x%29
The total interest paid will be
%2812%2F100%29+%2A+x+%2B+%2815%2F100%29+%2A+%2835000+-+x%29+=+4650 Multiply both sides of the equation by 100
12+%2A+x+%2B+15+%2A+%2835000+-+x%29+=+4650+%2A+100 Multiply out the 15+%2A+%2835000+-+x%29
12x+%2B+525000+-+15x+=+465000 Collate like terms
-3x+%2B+525000+=+465000 Subtract 525000 from each side
-3x+%2B+525000+-+525000+=+465000+-+525000
-3x++=+-+60000 Divide each side by -3
%28-3x%29%2F-3++++=+++%28-+60000%29+%2F+-3
x= $20 000 The rest of the $35 000 loan is held by the second person ie $15 000.

So the first person has a loan of $20 000 and the second person has a loan of $15 000.