Question

An investment of ​$42,000 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 $3480 The interest from the first investment was 6 times the interest from the second. Find the amounts of the three parts of the investment

Answer 1

Answer:The amounts of the three parts of the investment are:

x = $14,072.73

y = $3,127.27

z = $24,800

Explanation:

Let's assume that the first part of the investment is x.

Then the second part of the investment is y and the third part of the investment is z.

We know that the total investment is $42,000. Therefore:

x + y + z = 42,000

We also know that the total interest earned is $3,480. Therefore:

0.08x + 0.06y + 0.09z = 3,480

Finally, we know that the interest earned from the first investment is 6 times the interest earned from the second investment. Therefore:

0.08x = 6(0.06y)

0.08x = 0.36y

x = 4.5y

Now we can substitute x = 4.5y into the first equation:

4.5y + y + z = 42,000

5.5y + z = 42,000

We can also substitute x = 4.5y into the second equation:

0.08(4.5y) + 0.06y + 0.09z = 3,480

0.36y + 0.06y + 0.09z = 3,480

0.42y + 0.09z = 3,480

Now we have two equations with two variables. We can solve for y in the first equation:

5.5y + z = 42,000

5.5y = 42,000 - z

y = (42,000 - z)/5.5

We can substitute this expression for y into the second equation:

0.42y + 0.09z = 3,480

0.42((42,000 - z)/5.5) + 0.09z = 3,480

Simplifying this equation, we get:

3,818.18 - 0.07636z + 0.09z = 3,480

0.01364z = 338.18

z = 24,800

Now we can use this value of z to find y:

5.5y + z = 42,000

5.5y + 24,800 = 42,000

5.5y = 17,200

y = 3,127.27

Finally, we can use the values of y and z to find x:

x = 4.5y

x = 4.5(3,127.27)

x = 14,072.73