Bill and Rebecca are playing a game at an arcade. Bill starts the next round of the game with 30 points and earns 4 more points each round. Rebecca starts the next round with 60 points but loses 6 more points each round. Is there a time when they’ll have the same number of points?

Question

The equation below represents the number of points, y, that Rebecca has after x rounds. Use the equation to complete the table with the number of points Rebecca has after 2, 3, and 5 rounds. You can solve on paper and then enter your answer on Zearn.
y=60−6x

Rounds (x) Points (y)
2
3
5

Answer 1

To find out how many points Rebecca has after 2, 3, and 5 rounds using the equation \( y = 60 - 6x \), we can substitute the values of \( x \) into the equation.

1. For \( x = 2 \): \[ y = 60 - 6(2) = 60 - 12 = 48 \]

2. For \( x = 3 \): \[ y = 60 - 6(3) = 60 - 18 = 42 \]

3. For \( x = 5 \): \[ y = 60 - 6(5) = 60 - 30 = 30 \]

Now we can complete the table:

| Rounds (x) | Points (y) | |------------|------------| | 2 | 48 | | 3 | 42 | | 5 | 30 |

Thus, Rebecca's points after the specified rounds are:

• After 2 rounds: 48 points
• After 3 rounds: 42 points
• After 5 rounds: 30 points