Question

Danny spends `9/11` of the money he had and finds he has `$88` left. How much did have initially?

Answer 1

$484

Explanation:

Let `color(red)x` be the amount of money Danny had at first.

since Danny spent `color(red)(9/11)` of his money,
amount of money spent by him `= 9/11*x`
`therefore`money left with him `=x-9/11*x`

but we are given that he had `$88` left.

`=> x-9/11*x = 88`
`=> (11x-9x)/11 = 88`
`=>(2x)/11=88`
`=> x=88*11/2 = 44*11 = color(red)484`

`therefore` Danny initially had $484

Answer 2

He had `$484`

Explanation:

We can calculate this using direct proportion.

If he spends `9/11` , it means he has `2/11` of the money left.

If we know how much `2` parts is, we can find how much `9` parts is.

`2/9 = 88/x`

`x = (88 xx 9)/2`

`x = $484`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Or, you can increase `88` in the ratio `9 : 2`

`88 xx 9/2`

`=$484`

Answer 3

Initial sum was: `$484.00`

Explanation:

Let the initial value be `v`

Spent `9/11v`

Left `2/11v=$88.00`

`v=11/2xx$88.00=$484.00`