Trick or Treat
posted by Linda on .
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?

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
X6=10 and X = 16 which means the boy had 16 going into the 3rd "robber."
How many into the second?
(X/2)2 = 16
X4=16
X = 4=32
X = 36 going into the second.
(X/2)1 = 36
X2=72
X = 74 to start.
Check it.
1/2 of 74 = 37 and 371=36
1/2 of 36 = 18 and 182 = 16
1/2 of 16 = 8 and 83=5. 
74

74