A)
Well, in pre-calc Y must not have anything else on it's side of the equation (for ease in writing and solving), so say that X is 4 and Y is 8:
Y/8 = X/4 because 8/8 = 4/4 = 1. Now "transfer" the 8 to the other side: Y = 8/4xX now simplify and get Y = 2X. That would be how x relates to y and vice versa.
B) instead of it being Y = 2X, it's 1/2 Y = X, but since fractions aren't allowed, it's 0.5Y = X
C) Not as hard as it sounds, but it involves steps SIMILAR to the above:
-A box has six sides, an open one has five
-One is at the bottom
-Four are the actual sides
The area of the bottom (no top since it's open) sides is X times X (since Y is the height and each side is equal)
The area of each of the sides is X times Y, since the length of each side is X and the height is Y.
So, that means we have (X^2) times 1 and (XxY) times 4, thus the equation is: (X²) + 4(XY) = S
You can not have three variables here, so we use the 4000cm to solve for one of them, using the volume of this square-bottomed box, which is the base (X²) times the height (Y):
4000cm = X²Y
Y = 4000/(X²) (answer to B, this is a function of X, I'm not entirely sure what is different about part A)
Now plop that into the Y in "(X²) + 4(XY) = S" to get:
(X²) + 4(X)(4000/(X²)) = S
Simplified (cancellign out Xs):
(X²) + 16000/X = S
That should be the correct way.