SOLUTION: A box of stickers was shared among four children. Faith and Ayan took {{{1/2}}} of the stickers while Julia and Shafiq took the rest. Ayan had {{{1/3}}} as many stickers as Faith

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A box of stickers was shared among four children. Faith and Ayan took {{{1/2}}} of the stickers while Julia and Shafiq took the rest. Ayan had {{{1/3}}} as many stickers as Faith      Log On


   

Question 1184558: A box of stickers was shared among four children. Faith and Ayan took 1%2F2 of the stickers
while Julia and Shafiq took the rest. Ayan had 1%2F3 as many stickers as Faith. Faith had twice
as many stickers as Julia. Shafiq had 45 stickers more than Ayan. How many stickers
were there in the box at first?
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Let x be the number of stickers in the box.

Faith and Ayan took 1%2F2 of the stickers while Julia and Shafiq took the rest.
[1] F%2BA=%281%2F2%29x
[2] J%2BS=%281%2F2%29x

Ayan had 1%2F3 as many stickers as Faith.
[3] A=%281%2F4%29%281%2F2%29x+=+%281%2F8%29x
[4] F=%283%2F4%29%281%2F2%29x+=+%283%2F8%29x

Faith had twice as many stickers as Julia.
[5] J=%281%2F2%29%283%2F8%29x+=+%283%2F16%29x

Then from [2] and [5],
S=%285%2F16%29x

Shafiq had 45 stickers more than Ayan.
%285%2F16%29x=%281%2F8%29x%2B45
%285%2F16%29x=%282%2F16%29x%2B45
%283%2F16%29x=45
x=45%2F%283%2F16%29=45%2816%2F3%29+=+15%2A16=240

ANSWER: 240