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?

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Answer 1 · 2016-09-25T16:42:39

Carly had $818$ chocolates

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 · 2016-10-04T11:12:16

The number of chocolates she started with is 818

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

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

$?=818$