Question

An investment of $36,000 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 $2820 The interest from the first investment was 3 times the interest from the second. Find the amounts of the three parts of the investment. The First part of the investment was $______

Answer 1

Given:

The total investment = $36000.

The interest rate of the first investment = 8%.

The interest rate of the second investment = 6%.

The interest rate of the third investment = 9%.

The total interest = $ 2820.

The interest from the first investment was 3 times the interest from the second.

Required:

We need to find the amounts of the three parts of the investment.

Step-by-step explanation:

Let x, y, and z be the amounts of the three parts of the investment.

The total investment = $36000.

`x+y+z=36000`

The total interest = $ 2820.

`8\text{\% of x +6 \% of y + 9 \% of z = 2820}`
`(8)/(100)x+(6)/(100)y+(9)/(100)z=2820`
`0.08x+0.06y+0.09z=2820`

The interest from the first investment was 3 times the interest from the second.

`0.08x=3*0.06y`

`0.08x=0.18y`

Divide both sides by 0.08.

`(0.08x)/(0.08)=(0.18y)/(0.08)`

`x=2.25y`

`Substitute\text{ x=2.25y in the equation }0.08x+0.06y+0.09z=2820.`

`0.08(2.25y)+0.06y+0.09z=2820`

`0.18y+0.06y+0.09z=2820`

`0.24y+0.09z=2820`

`0.09z=2820-0.24y`

Divide both sides by 0.09.

`(0.09z)/(0.09)=(2820)/(0.09)-(0.24y)/(0.09)`

`z=31333.33-2.67y`

`Substitute\text{ x =2.25y and z=31333.33y-2.67y in the equation }x+y+z=36000.`
`2.25y+y+31333.33-2.67y=36000`

`2.25y+y-2.67y=36000-31333.33`

`0.58y=4666.67`

Divide both sides by 0.58.

`(0.58y)/(0.58)=(4666.67)/(0.58)`
`y=8045.98`

`Substitute\text{ y =8045.98 in the equation }x=2.25y.`
`x=2.25*8045.98`

`x=18103.46`

`Substitute\text{ }x=18103.46\text{, and y =8045.98 in the equation x+y+z=36000.}`
`18103.46+8045.98+z=36000`

`26149.44+z=36000`
`z=36000-26149.44`
`z=9850.56`

Final answer:

The first part of the investment was $ 18103.46.

The second part of the investment was $ 8045.98.

The third part of the investment was $ 9850.56