Question

Carly had some chocolates. She gave 178 chocolates to her neighbour and 2/5 of the remainder to her daughter. With the remaining chocolates, she gave 1/3 of the chocolates to her son and then had 256 chocolates left. How many chocolates had she at first?

Answer 1

Carly had `818` chocolates

Explanation:

Let Carly had `x` chocolates.

She gave `178` chocolates to her neighbour.

Remaining are `x-178` and as `2/5` of `(x-178)` were given to her daughter,

remaining were `1-2/5=(5-2)/5=3/5` of `(x-178)`

i.e. `(3(x-178))/5` are left

Now `1/3` of `(3(x-178))/5` were given to son

remaining were `1-1/3=(3-1)/3=2/3` of `(3(x-178))/5`

i.e. `2/3xx(3(x-178))/5` are left.

Hence `2/3xx(3(x-178))/5=256`

Hence, `x-178=256xx3/2xx5/3` or

`x-178=128cancel(256)xxcancel3/(1cancel2)xx5/cancel3=640`

and `x=640+178=818`

Carly had `818` chocolates

Answer 2

The number of chocolates she started with is 818

Explanation:

Breaking the question down into its component parts:

Carly had some chocolates: `-> ?`
She gave 178 to her neighbour: `->color(red)([?-178]" left(remainder)")`

`color(white)(.)`

`color(green)(2/5" of the remainder to her daughter:")`
`->color(red)([?-178]) color(green)(-2/5[?-178])" "color(purple)( =" "3/5[?-178]" left")`

`color(white)(.)`

`color(olive)("With the remaining she gave "1/3" to her son:")`
`->color(purple)(3/5[?-178])color(olive)(-1/3(3/5[?-178]))" "=" "2/5[?-178]" left"`

`color(white)(.)`
then she had 256 chocolates left:`->2/5[?-178]" "=" "256`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Cross multiply (same as multiply both sides by `5/2`

`[?-178]" "=" "5/2xx256`

Add 178 to both sides

`? =[5/2xx256]+178`

`?=818`