Bill and Hector are playing a game at an arcade. Bill starts the next round of the game with 10 points and earns 10 more points each round. Hector starts the next round with 100 points but loses 5 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 Hector has after x rounds. Use the equation to complete the table with the number of points Hector has after 4, 6, and 8 rounds. You can solve on paper and then enter your answer on Zearn.
y=100−5x

Rounds (x) Points (y)
4
6
8

Answer 1

To find the number of points Hector has after a certain number of rounds, we can use the equation provided:

\[ y = 100 - 5x \]

Now, we'll calculate Hector's points for \( x = 4 \), \( x = 6 \), and \( x = 8 \).

1. For \( x = 4 \): \[ y = 100 - 5(4) = 100 - 20 = 80 \]

2. For \( x = 6 \): \[ y = 100 - 5(6) = 100 - 30 = 70 \]

3. For \( x = 8 \): \[ y = 100 - 5(8) = 100 - 40 = 60 \]

Now we can fill out the table with Hector's points after 4, 6, and 8 rounds:

| Rounds (x) | Points (y) | |------------|------------| | 4 | 80 | | 6 | 70 | | 8 | 60 |

So, Hector has:

• 80 points after 4 rounds,
• 70 points after 6 rounds,
• 60 points after 8 rounds.