Question

An investment of ​$29,000 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 $ 2250. The interest from the first investment was 4 times the interest from the second. Find the amounts of the three parts of the investment.

Answer 1

The amounts of three parts of the investment are 18000, 6000, 5000 respectively.

Explanation:

An investment of ​$29,000 was made by a business club.

Let the amount of first and second investment be x and y respectively. So, the amount of third investment is (29000-x-y).

The first part of the investment earned​ 8% interest, the second​ 6%, and the third​ 9%. Total interest from the investments was $ 2250.

`0.08x+0.06y+0.09(29000-x-y)=2250`

On simplification we get

`-0.01x-0.03y+2610=2250`

`-0.01x-0.03y=2250-2610`

`-0.01x-0.03y=-360`

`0.01x+0.03y=360` ..... (1)

The interest from the first investment was 4 times the interest from the second.

`0.08x=4(0.06y)`

`0.08x=0.24y`

`x=3y` .... (2)

From (1) and (2) we get

`0.01(3y)+0.03y=360`

`0.03y+0.03y=360`

`0.06y=360`

Divide both sides by 0.06.

`y=6000`

Put this value in equation (2).

`x=3(6000)=18000`

The amount of third investment is

`29000-x-y=29000-18000-6000=5000`

Therefore the amounts of three parts of the investment are 18000, 6000, 5000 respectively.