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?

This is hardly calculus.

Assume the original money was in 24 parts. She spent 12 parts on clothes, she had 12 parts left. She spent 4 parts on games. She had 8 parts left. She spend 2 parts on toys. She had six parts left.

sixparts is 7777. What is the original 24 parts?

Ok, it is prealgebra, not calculus.

lol whatever it is. thanks =)

To find out how much money the girl earns every month, let's break down the problem step by step.

1. Start with the amount of money the girl had left after buying all the items, which is $7777.

2. Let's work backward to find the amount of money she had before buying toys. We know that after buying toys, she had $7777 left. We can use this information to calculate the amount she had before buying the toys. Since she spent 1/4 of the remaining money on toys, this means the remaining money was 4 times the amount spent on toys. So the remaining money before toys was $7777 x 4 = $31108.

3. Now let's find the amount of money she had before buying games. We know that after buying games, she had $31108. Since she spent 1/3 of the remaining money on games, this means the remaining money was 3 times the amount spent on games. So the remaining money before games was $31108 x 3 = $93324.

4. Finally, let's find the amount of money she had before buying clothes. We know that after buying clothes, she had $93324. Since she spent 1/2 of the remaining money on clothes, this means the remaining money was 2 times the amount spent on clothes. So the remaining money before clothes was $93324 x 2 = $186648.

5. Since we assumed she had no money at the beginning of last year and she saved her allowance up to that point, the amount of money she earned every month is the total amount she had before buying clothes divided by the number of months in a year. So the monthly allowance she earns is $186648 / 12 = $15554.

Therefore, the girl earns $15,554 every month.