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?

Question

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?

DrBob222 · Accepted Answer

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=16 X = 4=32 X = 36 going into the second. (X/2)-1 = 36 X-2=72 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.

chelsea · Answer

74

person · Answer

Just wondering how many people came here because their teacher gave u guys this problem?

HumanBeing · Answer

2(5+3) = 16 2(16+2) = 36 2(36+1) = 74 Billy had 74 pieces of candy at the beginning.

Explain Bot · Answer

To solve this problem, let's work backward. We know that Little Billy had 5 pieces of candy left after the Ninja Turtle stole some. So before the Ninja Turtle acted, he had (5 pieces + 3 pieces) = 8 pieces of candy. Now, let's figure out how much candy Little Billy had before the Shark stole some. We know that he had 8 pieces of candy when the Ninja Turtle stole some, so before the Ninja Turtle acted, Little Billy had (8 pieces + 2 pieces) = 10 pieces of candy. Finally, let's determine how much candy Little Billy had before Freddy Krueger took some. We know that he had 10 pieces of candy when the Shark took some, so before the Shark acted, Little Billy had (10 pieces + 1 piece) = 11 pieces of candy. Therefore, Little Billy had 11 pieces of candy before Freddy, the Shark, and the Ninja Turtle raided his sack.