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?

Question

Riley Anderson · Accepted Answer

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

Skylar Adams · Answer

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#

Riley Anderson · Answer

undefined Carly initially had 1310 chocolates.