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Question 163462: Derek brought raisins for lunch and shared them with some of his classmates. He gave half of his raisins to Mollythen ate one himself. After that he gave half of the remainng to Tricia and ate another on himself. Finally, he gave half of the remaining raisins to Clark, and had 7 raising left. Hoaw amny raisins did Derek start with?
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! Let x=number of raisins that Derek started with
Molly got x/2 raisins and he ate one which equals (x/2)+1
He now has x-((x/2)+1) remaining and this equals:
x-(x/2)-1=((x/2)-1)----remaining
Tricia got (1/2)((x/2)-1)=(x/4)-1/2 and he ate one which equals (x/4)-(1/2)+1=
(x/4)+1/2
He now has remaining:
(x/2)-1-((x/4+1/2)=
(x/2)-1-(x/4)-1/2=
(x/4)-3/2
Clark got (1/2)((x/4)-3/2)=(x/8)-3/4
He now has remaiining
(x/4)-3/2-((x/8)-3/4)=
(x/8)-3/2 + 3/4=(x/8)-3/4 and this we are told equals 7
So:
(x/8)-3/4=7 multiply each term by 8
x-6=56 subtract 6 from each side
x-6+6=56-6 collect like terms
x=50-----------------------number of raisins that Derek started with
CK:
Molly got 50/2=25 and he ate DISABLED_event_one= 24
so he had 26 left
Tricia got 26/2=13 and he ate DISABLED_event_one= 12
So he had 14 left
Clark got 14/2=7
and there's 7 left
Hope this helps---ptaylor
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