Too many school assignments

Question

This year we have to make our school assignments in pairs.
With each classmate must be made exactly one of those assignments.
Exactly 30% of the assignments will be made by a pair of girls.
How many assignments do I have to make?

Greedoid · Accepted Answer

Say we have $b$ boys and $g$ girls, then we have $${gchoose 2} = {3over 10}{b+gchoose 2}$$ so we have this equation $$3b^2 +3b(2g-1)= 7g(g-1)$$
Now for each $g$ find $b$. If we put $x = 2(b+g)-1$ and $y= 2g-1$ we get $$boxed{10y^2-7=3x^2}$$
Here are some values

TakingNotes · Answer

I'm not sure if this is the only possible solution to the puzzle, but I found that if:

Again, there may be more solutions based on the rules outlined in the puzzle.

Too many school assignments

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