+68 Braydon wanted to give each of his friends equal number of stickers for his birthday. if he give each friends 9 stickers, he will be short for 69 stickers. if he gave each friend 4 stickers, there will be 46 stickers left. How many sticekrs can Braydon actually give to each friend such that he has no remaining stickers left?
+313 Let the number of friend that Braydon have = x
Case 1: When he given 9 stickers to each friend.
Since he gave 9 stickers to each friend,
∴ Number of distributed stickers = 9x
While distributing 9 stickers to each friend he will be short for 69 stickers.
∴ The number of stickers Braydon actually have = 9x-69
Case 2 : When he given 4 stickers to each friend.
Since he gave 4 stickers to each friend,
∴ Number of distributed stickers = 4x
While distributing 4 stickers to each friend he will have 46 more tickets.
∴ The number of stickers Braydon actually have = 4x+46
Since Braydon have equal number of tickets in each case,
∴ 9x-69 = 4x+46
⇒ 9x-4x = 46+69
⇒ 5x = 115
⇒ x = 23
Hence there are 23 friends.
Number of stickers = 4x+46 = 4(23)+46 = 138
Now we know that there are 138 tickets in total and 23 friends.
Hence the number of tickets each friend will get such that no sticker remains = \({138 \over 23}{}{} = 6\)
Hence Braydon must given 6 tickets to each of his friend such that no sticker is left.
