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

Answer:

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

Step-by-step 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.