“In a line of 583 children, every 5 boys stand between 2 girls. How many boys are there?”
I suspect a major issue may be the interpretation of the problem. In addition, it's important to approach a problem starting with its meaning, not with an expected "tool" to be used to solve it.
So I'd start by thinking about what it means, which is a little ambiguous. We can start with this:
GBBBBBG
That's 5 boys between 2 girls.
Now, how do we continue? That's where we might disagree, but I think it is meant to look like this:
GBBBBBGBBBBBGBBBBBG
So we alternate 5 boys and 1 girl (not 2, as you may have been thinking). And there will be a girl at each end, which disrupts things a bit.
(I notice I disagree with Romsek; we can argue about that, if you wish, but my plan from the start was to see if my interpretation led to a reasonable answer - it does - and then try another if it didn't.)
I'm going to leave it there, with nothing but an interpretation. See what you can do with that, and write back showing us what methods you've tried (and how you are interpreting the problem now). I could suggest some specific things to do, but those are learned best if you (that is, the child) can figure them out for yourselves.