OK, let's not overthink it! If we say w is the number of weeks, then in 7 weeks, each makes $7w, right? Let's say I started with $10. After seven weeks, I'd have $(7w + 10). We normally leave off the $ because it just gets in the way. If two things are the same, they are equal.
2w + 12 = 6w - 4
16 = 4w
w = 4
4 weeks