SOLUTION: On her way home from school Gloria Sol met a friend and gave her one half of all her candy. Next, she met another friend and gave her one third of all the candy she had left. Then,

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Question 850241: On her way home from school Gloria Sol met a friend and gave her one half of all her candy. Next, she met another friend and gave her one third of all the candy she had left. Then, she met another friend and gave him one half of all the candy she had left. She then had 9 pieces left. How many pieces did she start with?
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
She started with some number, p of candy.
Gift 1: She now has p-p%2F2 candy pieces.
Gift 2: She has now %28p-p%2F2%29-%281%2F3%29%28p-p%2F2%29 candies.
Gift 3: candies she still possesses.

You could simplify each gift-step from 1 through 3, before simplifying and solving for p. That would be the most comfortable way.
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Result of Gift 1 is simply p%2F2.
Gift 2 results in p%2F2-%281%2F3%29%28p%2F2%29=p%2F2-p%2F6=3p%2F6-p%2F6=2p%2F6=highlight_green%28p%2F3%29.
Gift 3 gives the result p%2F3-%281%2F2%29%28p%2F3%29=2p%2F6-p%2F6=highlight_green%28p%2F6=9%29.
That is the way to go.
highlight%28p=9%2A6=54%29 pieces of candy at the beginning.