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

so solve it backwards in steps, for example, start with the last part, so if after spending 1/4 of the money she has $7777, the first step would be x-0.25x=7777 letting x equal the money she had before she spent one quarter of it on toys.

solve for x, and then take it the next step back and so on, is that making sense now?

Answer 2

indeed

Answer 3

$2222

Answer 4

Here's another way of thinking of this.
Let's say she had started with $100
After spending half, or 50% she ended up with 50%, or 50% of 100 = $50 left
Then after spending one third of the remaining money, 33.3333%, she is left with 66.666 %: 66.666% of $50 = $33.33333 left
Then she spent 25% of what was left. That means she kept 75% of what was left: 75% of $33.3333 = $25 left
That means after the three expenditures she has $25 out of $100, or 25%
That means that the $7777 she had left is 25% of the original amount.
If $7777 is 25% of original amount, what is 100% of original amount?
This proportion will give you the answer: $7777/25 = x/100

Answer 5

thx