Answer:
Barry has 15 dollars, Sherry 35 dollars and Perry 70 dollars.
Step-by-step explanation:
Let's start by setting Sherry's cash as a variable named x, Barry's cash named as y and Perry's cash named as z.
The 3 children together have 120$, meaning that the following equation is true:
![x + y + z = 120](https://tex.z-dn.net/?f=x%20%2B%20y%20%2B%20z%20%3D%20120)
If Barry (y) has 20$ less than Sherry (x), then we can conclude, that:
![y = x - 20](https://tex.z-dn.net/?f=y%20%3D%20x%20-%2020)
If Perry (z) has 2 times the amount of money Sherry (x) has, then we can conclude, that:
![z = 2x](https://tex.z-dn.net/?f=z%20%3D%202x)
If we replace all the y and z variable in the first equation with what we just made, we get a way easier equation than before:
![x + (x - 20) + (2x) = 120](https://tex.z-dn.net/?f=x%20%20%2B%20%28x%20-%2020%29%20%2B%20%282x%29%20%3D%20120)
We can easily remove the brackets and go on to solving the equation, giving us x, which is equal to how much money Sherry has:
![x + x - 20 + 2x = 120 \\ 4x - 20 = 120 \\ 4x = 140 \\ x = 35](https://tex.z-dn.net/?f=x%20%2B%20x%20-%2020%20%2B%202x%20%3D%20120%20%5C%5C%204x%20-%2020%20%3D%20120%20%5C%5C%204x%20%3D%20140%20%5C%5C%20x%20%3D%2035)
So, Sherry has 35$. Since Barry has 20$ less than 35$, we can conclude, that:
![35 - 20 = 15](https://tex.z-dn.net/?f=35%20-%2020%20%3D%2015)
Barry has 15$.
If Perry has 2 times the amount Sherry has, then we can conclude, that:
![2 \times 35 = 70](https://tex.z-dn.net/?f=2%20%5Ctimes%2035%20%3D%2070)
Perry has 70$.