SOLUTION: A bank loaned out $19,500, part of it at the rate of 2% annual interest, and the rest at 12% annual interest. The total interest earned for both loans was $2,140.00. How much was l

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Question 978671: A bank loaned out $19,500, part of it at the rate of 2% annual interest, and the rest at 12% annual interest. The total interest earned for both loans was $2,140.00. How much was loaned at each rate?
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Total amount of money invested: $19500
x+y=19500,
Total yearly interest for the two accounts is: $2140
0.02*x+0.12*y=2140
x=19500-y
Substitute for x
0.02*(19500-y)+0.12*y=2140
Multiply out
390-0.02*y+0.12*y=2140
Combine like terms.
0.1*y=1750
Isolate y
y=$ 17500.00 at 12% earns $2100 interest
x=19500-y
Calculate x
x=$ 2000.00 at 2% earns $40 interest
Check
0.02*2000+0.12*17500=2140
40+2100=2140
2140=2140
If 2140=2140 is TRUE and neither x nor y is negative then all is well
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