SOLUTION: I have a plate of whole cookies. I gave Tim half of what was on the plate, plus half of a cookie. I gave Beth half of what was left on the plate, plus half of a cookie. I gave Mich

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Question 331081: I have a plate of whole cookies. I gave Tim half of what was on the plate, plus half of a cookie. I gave Beth half of what was left on the plate, plus half of a cookie. I gave Michelle half of what was left on the plate, plus half of a cookie. I have no cookies left on my plate and I did not have to break any in half. How many cookies were on the plate to begin with?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let c = number of whole cookies on plate to begin with
I gave Tim c%2F2+%2B+1%2F2, so I have left
c+-+c%2F2+-+1%2F2+=+c%2F2+-+1%2F2
I gave Beth %281%2F2%29%2A%28c%2F2+-+1%2F2%29+%2B+1%2F2+=+c%2F4+-+1%2F4+%2B+1%2F2, so I have left
c%2F2+-+1%2F2+-+c%2F4+%2B+1%2F4+-+1%2F2+=+c%2F4+-+3%2F4
I gave Michelle %281%2F2%29%2A%28c%2F4+-+3%2F4%29+%2B+1%2F2+=+c%2F8+-+3%2F8+%2B+1%2F2
There are no cookies left on the plate
That means I gave away all the cookies, so
Tim, Beth, and Michelle have them all, so
c%2F2+%2B+1%2F2+%2B+c%2F4+%2B+1%2F4+%2B+c%2F8+%2B+1%2F8 = all the cookies
7c%2F8+%2B+7%2F8 = all the cookies
and, since
c = number of whole cookies on plate to begin with,
c+=+7c%2F8+%2B+7%2F8
c%2F8+=+7%2F8
c+=+7
There were 7 cookies on the plate to begin with
check answer:
I gave Tim 7%2F2+%2B+1%2F2+=+4, so I have 3 left
I gave beth 3%2F2+%2B+1%2F2+=+2, so I have 1 left
I gave Michelle 1%2F2+%2B+1%2F2+=+1, so I have 0 left
OK