Interests and Amounts Every month, a girl gets An allowance. Assume last year she had no money, and kept all the money she has earned up to now. Then she spends $\frac{1}{2}$ of her money on clothes, then $\frac{1}{3}$ of the remaining money on games, and then $\frac{1}{4}$ of the remaining money on toys. After she bought all of that, she had $7777$ left. Assuming she only gets money by allowance, how much money does she earn every month? 

Solution without equations, only fractions. If we represent by $1$ the
total money earned by the girl before spending on cloths, games and toys, we
can split this unit according to the fractions she spent:
$$1=\overset{3/4}{\overbrace{\underset{2/3}{\underbrace{\frac{1}{2}+\frac{1}{3}
\cdot \frac{1}{2}}}+\frac{1}{4}\cdot \frac{1}{3}}}+\frac{1}{4}$$
The fraction $\frac{1}{4}$ represents the money left, which we know is $7777
$. So the money she earned in a year is $4\cdot 7777$. An in a month $4\cdot
7777\cdot \frac{1}{12}=\frac{7777}{3}$.
