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# Math

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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?

Aug 9, 2021

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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.

Aug 9, 2021