An investment of $81 comma 000 was made by a business club. The investment was split into three parts and lasted for one year. The first part of the investment earned 8% interest, the second 6%, and the third 9%. Total interest from the investments was $ 6390. The interest from the first investment was 6 times the interest from the second. Find the amounts of the three parts of the investment.

First Part = $54,000

Second Part = $12,000

Third Part = $15,000

Explanation:

Let the first part be "x"

2nd part be "y", and

3rd part be "z"

Total money is 81,000, thus we can write:

x + y + z = 81000

Now, total interest is 6390 from each part with respective percentages, so we can write:

0.08x + 0.06y + 0.09z = 6390

Also,

Interest from 1st is 6 times interest from 2nd, so we can write:

0.08x = 6* (0.06y)

0.08x = 0.36y

x = 4.5y

Now replacing this in 2nd equation, we get:

0.08x + 0.06y + 0.09z = 6390

0.08(4.5y) + 0.06y + 0.09z = 6390

0.36y + 0.06y + 0.09z = 6390

0.42y + 0.09z = 6390

replacing x = 4.5y into 1st equation, we get:

x + y + z = 81000

4.5y + y + z = 81000

5.5y + z = 81000

Multiplying this by -0.09, we have:

-0.09 * (5.5y + z = 81000)

= -0.495y - 0.09z = -7290

Adding this and previous equation:

0.42y + 0.09z = 6390

-0.495y - 0.09z = -7290

-0.075y = -900

y = 12000

x = 4.5y

So,

x = 4.5(12,000) = 54000

x = 54000

z would be:

12000 + 54000 + z = 81000

z = 15000