Question

An investment of ​$57 comma 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 $ 4290. The interest from the first investment was 3 times the interest from the second. Find the amounts of the three parts of the investment.Investment 1 =

Investment 2 =
Investment 3 =

Answer 1

Inv 1: 36000

Inv 2: 16000

Inv 3: 5000

Explanation:

You can solve this, using an equation system.

Let's call the parts of the investment as "x" the first part, "y" the second part and "z" the third part.

We know that the investment is 57000$, so, the first equation would be the sum of the 3 parts:

x + y + z = 57000 (1)

Now, we also know the earn of all part. For x, is 8% (or 0,08), for y, 6% (or 0,06) and z is 9% (0,09). Finally the total interest is 4290. So second equation is:

0,08x + 0,06y + 0,09z = 4290 (2)

Finally, we know that x is three times the amount of y, so, the third and last equation is:

0,08x = 3 * 0,06y ----> 0,08x - 3 * 0,06y = 0 (3)

Now, to work better, let's use round numbers, equation 2 and 3, we will multiply them by 100, so:

0,08x + 0,06y + 0,09z = 4290 (2)

0,08x - 3 * 0,06y = 0 (3)

8x + 6y + 9z =429000 (2)

8x - 18y = 0 (3)

Now, let's put together all 3 equations:

x + y + z = 57000 (1)

8x + 6y + 9z =429000 (2)

8x - 18y = 0 (3)

Now, we just need to solve these equations, for any method you know.In this case, I will solve using sustitution:

From (3):

8x = 18y ---> x = 18/8 y = 9/4 y ---> This would be (4)

Replace (4) in (1):

9/4 y + y + z = 57000

13/4y + z = 57000

z = 57000 - 13/4y ---> This would be (5)

Now, replace (5) in (2), to solve the value of z:

8(9/4y) + 6y + 9(57000 - 13/4y) = 429000

72/4y + 6y + 513000 - 117/4y = 429000

18y + 6y - 117/4y = 429000 - 513000

24y - 29,25y = -84000

-5.25y = -84000

y = 84000/5.25 ----->y = 16000 $

With this value, replace in (4) to get x:

x = 9/4 * 16000 -----> x = 36000$

Finally, replace y in (5) to get z:

z = 57000 - 13/4(16000) -----> z = 5000$