Answer:
- $54000 was invested at 8% interest
- $36000 was invested at 6% interest
- $10000 was invested at 9% interest
Step-by-step explanation:
Total Investment = $100,000
The investment was split into three parts (say x, y and z)
Simple Interest = Principal X Rate/100 X Time
The first part of the investment earned 8% interest
Interest on the first part = 0.08x
The second part of the investment earned 6% interest
Interest on the second part = 0.06y
The third part of the investment earned 9% interest
Interest on the third part = 0.09z
Total interest from the investments = $ 7380.
Therefore:
0.08x+0.06y+0.09z=7380
The interest from the first investment was 2 times the interest from the second.
0.08x=2 X 0.06y
0.08x=0.12y
Substituting we have:
0.12y+0.06y+0.09z=7380
0.18y+0.09z=7380
From 0.08x=0.12y
x=1.5y
Substituting x=1.5y into x+y+z=100000
1.5y+y+z=100000
2.5y+z=100000
z=100000-2.5y
Substituting z=100000-2.5y into 0.18y+0.09z=7380
0.18y+0.09(100000-2.5y)=7380
0.18y+9000-0.225y=7380
-0.045y=-1620
Divide both sides by -0.045
y=36000
Recall: x=1.5y
x=1.5 X 36000
x =54000
x+y+z=100000
54000+36000+z=100000
z=100000-(54000+36000)
z=10,000
Therefore:
- $54000 was invested at 8% interest
- $36000 was invested at 6% interest
- $10000 was invested at 9% interest
