Answer: $14500 was loaned at 6%.
Step-by-step explanation:
Let x represent the amount loaned out at 6% interest rate.
Let y represent the amount loaned out at 14% interest rate.
The bank loaned out $19000, part of it at the rate of 6% per year and the rest at 14% per year. It means that
x + y = 19000
The interest received made from $x in one year is
6/100 × x = 0.06x
The interest received made from $y in one year is
14/100 × x = 0.14y
If the interest received in one year totaled $1500, it means that
0.06x + 0.14y = 1500- - - - - - - - - 1
Substituting x = 19000 - y into equation 1, it becomes
0.06(19000 - y) + 0.14y = 1500
1140 - 0.06y + 0.14y = 1500
- 0.06y + 0.14y = 1500 - 1140
0.08y = 360
y = 360/0.08
y = 4500
x = 19000 - y = 19000 - 4500
x = $14500
