Question

Billie and his friends are playing a board game where you go forward on the board if you throw an even number on a pair of dice, and backwards if you throw an odd number on a pair of dice. Billie's first throw is a 12, and his second throw is a 9, his third throw is an 8, and his fourth throw is a 4. How far has Billie gone from the start of the board game? (If you throw odd numbers that would take you off the board, you stay at the starting point.) Explain how you got your answer.

Answer 1

Billie's progress can be calculated step by step based on his dice throws:

1. First throw: 12 (even) - Move forward.
2. Second throw: 9 (odd) - Stay at the starting point (no movement as per the rules).
3. Third throw: 8 (even) - Move forward.
4. Fourth throw: 4 (even) - Move forward.

Since Billie moved forward on the first and third throws and stayed at the starting point on the second throw, his net progress is 12 - 9 + 8 + 4 = 15 spaces forward from the start of the board game.

Answer 2

Billie has gone 15 spaces forward from the start of the board game.

Explanation:

In this board game, Billie goes forward if he throws an even number on a pair of dice and backward if he throws an odd number. Additionally, if he throws odd numbers that would take him off the board, he stays at the starting point.

First Throw (12)

Since 12 is an even number, Billie moves forward 12 spaces.

Second Throw (9)

Since 9 is an odd number, Billie moves backward 9 spaces.

Therefore, Billie is now 12 - 9 = 3 spaces from the start of the board.

Third Throw (8)

Since 8 is an even number, Billie moves forward 8 spaces.

Therefore, Billie is now 3 + 8 = 11 spaces from the start of the board.

Fourth Throw (4)

Since 4 is an even number, Billie moves forward 4 spaces.

Therefore, Billie is now 11 + 4 = 15 spaces from the start of the board.

To find out how far Billie has gone from the start of the board game in one calculation, we add up his movements, ensuring we subtract the number of spaces he moves backward:

`\begin{aligned}\sf Net \;Distance& = 12 - 9 + 8 + 4\\&=3+8+4\\&=11+4\\&=15\end{aligned}`

Therefore, Billie has gone 15 spaces forward from the start of the board game.