Answer:
$4 million, $6 million and $20 million
Step-by-step explanation:
Let's denote the amounts invested by the first person, the second person, and the third person as x, y, and z, respectively.
According to the given information:
1. The first two people invest in the ratio 2:3. This means the ratio of their investments is 2/3.
So we can write:
x/y = 2/3 ----(1)
2. The third person invests twice as much as the other two combined. The total investment of the first two people is x + y.
So we can write:
z = 2(x + y) ----(2)
3. The total investment is $30 million.
x + y + z = 30 ----(3)
To solve this system of equations, we can use substitution or elimination method.
Let's start with the substitution method:
From equation (2), we have:
x + y = z/2 ----(4)
Substitute equation (4) into equation (3):
z/2 + z = 30
Multiply both sides by 2 to get rid of the fraction:
z + 2z = 60
3z = 60
z = 60/3
z = 20
Now substitute the value of z into equation (2):
20 = 2(x + y)
10 = x + y ----(5)
We now have two equations: (1) and (5).
From equation (1):
x/y = 2/3
Rearrange it as:
3x = 2y
Substitute the value of x from equation (5) into the above equation:
3(10 - y) = 2y
30 - 3y = 2y
30 = 5y
y = 30/5
y = 6
Substitute the value of y into equation (5):
10 = x + 6
x = 10 - 6
x = 4
So, the first person invested $4 million, the second person invested $6 million, and the third person invested $20 million.