If x+y= 15, y+z=25, and x+z=20, what is the arithmetic mean of x, y, and z

X + y = 15
Rearrange this to isolate for x.
x = 15 - y

x + z = 20
Rearrange this to isolate for x also.
x = 20 - z

Since they are both equal to x, that means they are equal to each other (x = x)

Set them equal to each other. 

15 - y = 20 - z
Now, isolate for y.

y = 15 - 20 + z

Now, use y + z = 25 and isolate for y.
y = 25 - z

Since they are both equal to y, we set them equal to each other.

15 - 20 + z = 25 - z
Solve for z
z + z = 25 - 15 + 20
2z = 30
2z/2 = 30/z
z = 15

Now you can plug the value for z into the other equations to find y and x.

x + z = 20
x +15 = 20
x = 20-15
x = 5

y + z = 25
y + 15 = 25
y = 25 - 15
y = 10