Answer: $9500 was loaned at 12%
$8000 was loaned at 10%.
Explanation:
Let x represent the amount which the bank loaned out at the rate of 12% annual interest.
Let y represent the amount which the bank loaned out at the rate of 10% annual interest..
The bank loaned out $17,500, part of it at the rate of 12% annual interest, and the rest at 10% annual interest. . This means that
x + y = 17500
The formula for determining simple interest is expressed as
I = PRT/100
Considering the amount loaned out the rate of 12% annual interest.
P = $x
T = 1 year
R = 12℅
I = (x × 12 × 1)/100 = 0.12x
Considering the amount loaned out the rate of 10% annual interest,
P = $y
T = 1 year
R = 10℅
I = (y × 10 × 1)/100 = 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