Algebra variations help needed?

Question

Ok..these wonderful word problems... I'm really getting too old for this..LOL

The surface area of a square cube varies directly as the square of thelength of an edge. The surface area is 24 ft^2 when the length of an edge is 2 ft. Find the surface area of a cube with an edge that is 5 ft.

Note** Please "show" me all the steps. I'm a VERY literal thinker and very visual learner. Don't assume I know ANYTHING (even basic) about algebra in your answer, that way I don't "miss" a thing. Thank you so much for your time and patience, it's been a "few" years :D

Answer 1

"Translate" that first sentence, piece by piece:

"The surface area of a square cube" -- just write "A"

"varies directly as" -- write "= k*" (that's what "varies directly" means, where k is an currently-unknown constant)

"the square of the length of an edge" -- if we let L denote the length of an edge, then this is L²

Now put the pieces together:

A = k*L²

Next, you are told that, for a particular case, A = 24 when L = 2; this enables you to determine the value of k:

24 = k*(2)²

24 = 4k

6 = k

So

A = 6L²

Finally, you are asked to calculate A (now that we know k) when L = 5 ft. Your answer should be in ft².