SOLUTION: Chuck receives loans totaling $12,000 from two banks. One bank charges 7.5% annual interest, and the second bank charges 9% annual interest. He paid $960 in total interest in one y

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Chuck receives loans totaling $12,000 from two banks. One bank charges 7.5% annual interest, and the second bank charges 9% annual interest. He paid $960 in total interest in one y      Log On


   



Question 234701: Chuck receives loans totaling $12,000 from two banks. One bank charges 7.5% annual interest, and the second bank charges 9% annual interest. He paid $960 in total interest in one year. How much was loaned at each bank ?
could you show me how to set up the equation for this.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for simple interest is
A+=+P%2A%281+%2B+rt%29
A = amount after t years
r = interest rate
P = original amount
-------------------------------
Let x = amount loaned by 1st bank
Then 12000+-+x will be the amount loaned by other bank
bank 1:
r+=+.075
P%5B1%5D+=+x
A%5B1%5D+=+x%2A%281+%2B+.075%2A1%29
A%5B1%5D+=+1.075x
---------------
bank 2:
r+=+.09
A%5B2%5D+=+%2812000+-+x%29%2A%281+%2B+.09%2A1%29
A%5B2%5D+=+1.09%2A%2812000+-+x%29
A%5B2%5D+=+13080+-+1.09x
---------------
The interest paid to bank 1 is A%5B1%5D+-+P%5B1%5D
The interest paid to bank 2 is A%5B2%5D+-+P%5B2%5D
The total interest paid to the two banks is
%28A%5B1%5D+%2B+A%5B2%5D%29+-+%28P%5B1%5D+%2B+P%5B2%5D%29
The total interest paid is $960
%28A%5B1%5D+%2B+A%5B2%5D%29+-+%28x+%2B+12000+-+x%29+=+960
1.075x+%2B+13080+-+1.09x+-+12000+=+960
-.015x+%2B+1080+=+960
-.015x+=+-120
x+=+8000
12000+-+x+=+12000+-+8000
12000+-+x+=+4000
$8000 was loaned at bank 1
$4000 was loaned at bank 2
check answer:
A%5B1%5D+=+x%2A%281+%2B+.075%2A1%29
A%5B1%5D+=+8000%2A1.075
A%5B1%5D+=+8600
and
A%5B2%5D+=+1.09%2A%2812000+-+x%29
A%5B2%5D+=+1.09%2A4000
A%5B2%5D+=+4360
and
%28A%5B1%5D+%2B+A%5B2%5D%29+-+%28P%5B1%5D+%2B+P%5B2%5D%29+=+960
8600+%2B+4360+-+8000+-+4000+=+960
12960+-+12000+=+960
960+=+960
OK