I could not find any useful information on "ratio box", so I'm not sure what that means, either.
Sometimes, Denis is too slick. Don't feel bad if you cannot understand his response; at first glance, I don't understand it either.
Subhotosh posted an algebraic relationship.
I realize that you did not post on one of the algebra boards, but algebra is the only tool I can come up with right now for this exercise.
If you could explain a "ratio box" example given to you, then maybe I could come up with something else.
Anyway, here is the algebraic solution. If you're not interested, feel free to ignore it.
You're looking for two numbers that add to make 1260 and divide to make 7/5.
Let the symbol W represent the number of winners.
Let the symbol L represent the number of losers.
The given information that "the ratio of winners to losers is 7/5" gives the following.
W/L = 7/5
The given information that "the total number of winners and losers is 1260" gives the following.
W + L = 1260
If we subtract the number of winners from 1260, then we get an expression for the number of losers written with the symbol W.
L = 1260 - W
We can replace the symbol L in the ratio with the expression 1260 - W.
W/L = 7/5
W/(1260 - W) = 7/5
When two fractions (ratios) are equal, we can "cross multiply".
W * 5 = 7 * (1260 - W)
We multiply the right-hand side using a rule called The Distributive Property.
5W = (7)(1260) - 7W
5W = 8820 - 7W
Add 7W to both sides.
5W + 7W = 8820 - 7W + 7W
12W = 8820
Divide both sides by 12.
12W/12 = 8820/12
W = 735
The number of winners is 735.
1260 - 735 = 525
The number of losers is 525
CHECK THE RESULTS.
735/525 = 7/5
735 + 525 = 1260
It checks.
Again, if you understand little of what I typed because you have not seen algebra before, that's not your fault. Just ignore it. Perhaps, with the answers, you can work backwards to figure out your ratio-box method.
If not, then try to explain a ratio box example, and we'll go from there.