Answer: $9500 was loaned at 12% and $8000 was loaned at 10%
Step-by-step explanation:
Let x represent the amount that the
bank loaned out at the annual rate of 12%.
Let y represent the amount that the
bank loaned out at the annual rate of 10%.
The bank loaned out $17,500, part of it at the rate of 12% annual interest, and the rest at 10% annual interest.. It means that
x + y = 17500
The interest on $x after 1 year would be
12/100 × x = 0.12x
The interest on $y after 1 year would be
10/100 × y = 0.1y
The total interest earned for both loans was $1,940.00. . It means that
0.12x + 0.1y = 1940- - - - - - - - - 1
Substituting x = 17500 - y into equation 1, it becomes
0.12(17500 - y) + 0.1y = 1940
2100 - 0.12y + 0.1y = 1940
- 0.12y + 0.1y = 1940 - 2100
- 0.02y = - 160
y = - 160/ - 0.02
y = 8000
x = 17500 - y = 17500 - 8000
x = $9500
