Emma and her friends played a board game that uses cards and dice to determine how many spaces they move. On her first turn, Emma rolled the dice and then played a card that increased the number of spaces she moved by 8. On her second turn, she rolled 3 times her previous roll, but her friend played a card that decreased the number of spaces she moved by 4. In the end, she moved the same number of spaces on both turns.

Question

Which equation can you use to find r, the number Emma rolled on her first turn?

r+8=3r-4

r+8=3r+4

Answer 1

To determine the right equation for the problem, let's break down Emma's movements.

1. On her first turn, Emma rolled a number $r$ and moved $r+8$ spaces (since a card increased her movement by 8).
2. On her second turn, she rolled 3 times her previous roll, so she moved $3r$, but her friend played a card that decreased her movement by 4 spaces, resulting in her moving $3r-4$ spaces.

Since it's given that she moved the same number of spaces on both turns, we can set up the equation:

$$r+8=3r-4$$

This means the correct equation to find $r$ is:

$r+8=3r-4$