Answer:
Inv 1: 36000
Inv 2: 16000
Inv 3: 5000
Step-by-step 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$
