Trick or Treat

Little Billy was out trick or treating on Halloween. He had gotten a lot of candy and was peering into his bag, when out from behind a tree came Freddy Krueger. Freddy reached into Billy's bag and took half of his candy plus one piece. Within a few steps, Billy encountered a Great White Shark, who reached into Billy's sack and took half of his remaining candy plus two pieces. Before Billy could turn and run, a Ninja Turtle, stole half of the candy that was left plus three pieces. Now Little Billy began to cry because he only had 5 pieces of candy left. How many pieces of candy did Billy have before Freddy, the Shark, and the Ninja Turtle raided his sack?

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  1. I would do that this way.
    Let X = candy from 3rd party.
    (X/2)-3 = 5
    Solve for X and I get 16 as follows:
    Multiply through by 2
    X-6=10 and X = 16 which means the boy had 16 going into the 3rd "robber."
    How many into the second?
    (X/2)-2 = 16
    X = 4=32
    X = 36 going into the second.

    (X/2)-1 = 36
    X = 74 to start.

    Check it.
    1/2 of 74 = 37 and 37-1=36
    1/2 of 36 = 18 and 18-2 = 16
    1/2 of 16 = 8 and 8-3=5.

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  2. 74

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