SOLUTION: Danny had some stickers. He gave one-third of the stickers plus 1 sticker to his brother. Then he gave one-third or the remaining stickers plus 4 stickers to his sister. Finally, h

Algebra ->  Equations -> SOLUTION: Danny had some stickers. He gave one-third of the stickers plus 1 sticker to his brother. Then he gave one-third or the remaining stickers plus 4 stickers to his sister. Finally, h      Log On


   

Question 1012831: Danny had some stickers. He gave one-third of the stickers plus 1 sticker to his brother. Then he gave one-third or the remaining stickers plus 4 stickers to his sister. Finally, he gave one-half of what remained plus 3 stickers to his best friend. He found that he had 4 stickers left. How many stickers did Danny have at first?

Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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Start at the end and work backwards.
Danny has 4 stickers.
"He gave one-half of what remained plus 3 stickers to his best friend."
If he takes back the extra 3, he has 7 (which is half) and his friend has seven.
If he takes back 7, he has 14.
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He gave one-third of the remaining stickers plus 4 stickers to his sister
If he takes back the 4, he has 18.
This is two thirds of what he had before he gave 1/3 to sister,
so the 1/3 he gave sister was 9.
If he takes back 9, he has 27.
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He gave one-third of the stickers plus 1 sticker to his brother.
If he takes back the 1, he has 28.
This is two thirds of what he had before he gave 1/3 to brother,
so the 1/3 he gave brother was 14.
If he takes back 14, he has 42.
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highlight%28ANSWER%3A+Danny_started_with_42_stickers%29
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CHECK: (Go through it forward)
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He had 42 to start.
He gave 1/3 + 1 to brother
1/3(42)+1=14+1=15
42-15=27
He has 27 after brother.
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He gave 1/3 + 4 to sister.
1/3(27)+4=9+4=13
27-13=14
He has 14 left after sister.
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He gave 1/2 + 3 to friend.
1/2(14)+3=7+3=10
14-10=4
He has 4 left after friend.
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Exactly as he should.