Answer:The amounts of the three parts of the investment are:
x = $14,072.73
y = $3,127.27
z = $24,800
Explanation:
Let's assume that the first part of the investment is x.
Then the second part of the investment is y and the third part of the investment is z.
We know that the total investment is $42,000. Therefore:
x + y + z = 42,000
We also know that the total interest earned is $3,480. Therefore:
0.08x + 0.06y + 0.09z = 3,480
Finally, we know that the interest earned from the first investment is 6 times the interest earned from the second investment. Therefore:
0.08x = 6(0.06y)
0.08x = 0.36y
x = 4.5y
Now we can substitute x = 4.5y into the first equation:
4.5y + y + z = 42,000
5.5y + z = 42,000
We can also substitute x = 4.5y into the second equation:
0.08(4.5y) + 0.06y + 0.09z = 3,480
0.36y + 0.06y + 0.09z = 3,480
0.42y + 0.09z = 3,480
Now we have two equations with two variables. We can solve for y in the first equation:
5.5y + z = 42,000
5.5y = 42,000 - z
y = (42,000 - z)/5.5
We can substitute this expression for y into the second equation:
0.42y + 0.09z = 3,480
0.42((42,000 - z)/5.5) + 0.09z = 3,480
Simplifying this equation, we get:
3,818.18 - 0.07636z + 0.09z = 3,480
0.01364z = 338.18
z = 24,800
Now we can use this value of z to find y:
5.5y + z = 42,000
5.5y + 24,800 = 42,000
5.5y = 17,200
y = 3,127.27
Finally, we can use the values of y and z to find x:
x = 4.5y
x = 4.5(3,127.27)
x = 14,072.73