how many cookies were there to begin with

Question

three brothers found a plate of cookies that their mother had made them for later. they decided to take some and figured out how many each would take according to his age. as it turned out bill took 1/4 of them joe took 1/6 of them and harry took 1/12 of them. after the boys left, one of their sisters, kara, found the remaining cookies and took 1/3 of them. a little while later sucie came in and took 1/4 of kara left behind. finally a while later, beth cam ein and took 1/6 of the remaining cookies. this left 10 cookies on the plate. how many were on the plate to begin with?

Answer 1

let the whole plate of cookies = c

amount taken by the 3 boys = 1/4 + 1/6 + 1/12 = 3/12 + 2/12 + 1/12 = 6/12 

the whole is 12/12 so the balance left is 1/2 C

 

kara takes 1/3 so she leaves 2/3*1/2 = 1/3 C

 

sucie takes 1/4 of 1/3 C = 1/12 C 

 

beth takes 1/6 so she leaves 5/6 of 1/12 C = 5/72 C  which is = 10

 

solve for C 

number of cookies to start  = 144

 

now check