Every month, a girl gets allowance. Assume last year she had no money, and kept it up to now. Then she spends 1/2 of her money on clothes, then 1/3 of the remaining money on games, and then 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?

Question

anonymous · Answer

Let monthly allowance be $X. Last year she saved $12X.

She then spent $6X on clothes (50% of her starting amount), leaving $6X

She then spent 1/3 of this (i.e. $2X) on games, leaving $4X

She then spent 1/4 of this (i.e. $X) on toys, leaving $3X

So $3X = $7,777 and $X = $2,592.33

This monthly allowance looks a bit odd. Was I right in assuming she saved for 12 months, spending nothing last year?