Answer: $11100 was loaned at 9%
Step-by-step explanation:
Let x represent the amount that the
bank loaned out at the annual rate of 9%.
Let y represent the amount that the
bank loaned out at the annual rate of 19%.
The bank loaned out $19,000, part of it at the rate of 9% per year and the rest at 19% per year. It means that
x + y = 19000
The interest on $x after 1 year would be
9/100 × x = 0.09x
The interest on $y after 1 year would be
19/100 × y = 0.19y
If the interest received in one year totaled $2500. It means that
0.09x + 0.19y = 2500- - - - - - - - - 1
Substituting x = 19000 - y into equation 1, it becomes
0.09(19000 - y) + 0.19y = 2500
1710 - 19000y + 0.19y = 2500
- 0.09y + 0.19y = 2500 - 1710
- 0.1y = - 790
y = - 790/- 0.1
y = $7900
x = 19000 - y = 19000 - 7900
x = $11100
