Question 204859: I have a plate of WHOLE cookies; I gave Jodie 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. There are no cookies left, and I didn’t break any in half. How many cookies were on the plate to begin with?
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Well, I tried 7 cookies and that seems to work, and I know that this is not an algebraic answer, but I think that it can be worked out.
Start with 7.
To Jodie, half of 7 is 3.5 plus 0.5 = 4 so there are 3 cookies left.
To Beth, half of 3 is 1.5 pus 0.5 = 2, so now there is 1 cookie left.
To Michelle, half of 1 is 0.5 plus o.5 = 1, no more cookies left and no cookies needed to be broken.
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How did I get 7? Read on!
Let x = the original number of whole cookies on the plate.
To Jodie, you gave:
 what was left after that can be expressed by:
 let's call this quantity y, so...
To Beth, you gave:
 what was left after that can be expressed by:
 let's call this quantity z, so...
To Michelle, you gave:
 what was left after that can be xepressed by:
 ...and, because there were no cookies left, we'll call this zero, so...
 Now we can solve this for z: First simplify it.
 Multiply both sides by 2.
 Add 1 to both sides.
 Now we know z, we can solve for y.
 Finally, we can solve for x, the original number of cookies.
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