An investment of 63000 was made by a business clubThe invest

An investment of 63000 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,second 6% and third 9%.Total interest from the investment was 4950.The interest was 4 times the interest from the second.Find the amounts of the three parts of investment.

1.The amount from the first part of the investment.

2.the amount from the second part of the investment.

3.the amount from the third part of the investment.

Solution

Investment = 63,000
Interest I1 = x * 0.08 where \'x\' is the first part of the investment
Interest I2 = y * 0.06 where \'y\' is the second part of the investment
Interest rate I3 = z * 0.09 where \'z\' is the third part of the investment

We need to find x, y and z.
With the conditions given, we have

x + y + z = 63,000
I1 + I2 + I3 = 4950
I1 = 4 * I2

Hence we have

x + y + z = 63,000-------------------------- (1)
x * 0.08 + y * 0.06 + z * 0.09 = 4950 (2)
x * 0.08 = 4* y * 0.06---------------------- (3)

If we multply (3) from both sides by 100 and divide by 8 we get

x = 3y

From (1) we get z = 63,000 - x - y

z = 63,000 - 3y - y
z = 63,000 - 4y

Using x = 3y and z = 63,000 - 4y in (2) we get
3y * 0.08 + y * 0.06 + (63,000 - 4y) * 0.09 = 4950 *100

24 y + 6 y + 567,000 - 36 y = 495,000
6 y = 567,000 - 495,000
6 y = 72,000
y = 12,000

x = 3 * 12,000 = 36,000

z = 63,000 - 4 * 12,000 = 15,000

The first part of the investment is 36,000, the second part of the investment is 12,000 and the third part of the investment is 15,000.