Question

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?

Answer 1

Let's say she started with x dollars.
(1/2)x is what she had after clothes.
(1/3)(1/2)x is what she had after games.
(1/4)(1/3)(1/2)x is what she had after toys and that equals 7777

so, (1/4)(1/3)(1/2)x = 7777
Divide 7777 by (1/4)(1/3)(1/2) and you should get your answer. You can check by working through the problem with the value you get.

Answer 2

Correction ....

Answer 3

She has (2/3)(1/2)x after games
and (3/4)(2/3)(1/2)x after toys.

Answer 4

Anyway, sorry about that ....

(3/4)(2/3)(1/2) equals 6/24 or 1/4.

Dividing 7777 by 1/4 is the same as multiplying by 4 which results in 31,108.

Which, of course needs to be divided by 12 to find out her monthly allowance.