Questions about ratios

Question

At a school dance, each boy danced with exactly three girls and each girl danced with exactly two boys. if 100 boys attended the school dance, how many girls attended?

Answer 1

Hint:

Let $(b_1, b_2, \dots b_{100})$ be a set of boys and $(g_1, g_2, \dots g_{n})$ be a set of girls. IF $a_1$ dances with $g_1, g_2$ and $g_3$, he can't dance anymore. But $g_1, g_2$ and $g_3$ can dance for once more with a guy. Let $g_1, g_2, g_3$ dance with $a_2$. Now you must have new set of girls: $(g_4, g_5, g_6)$ they dance with $(a_3, a_4)$. Do you see a pattern here?