Jillian and Clarissa are playing a game at an arcade. Jillian starts the next round of the game with 10 points and earns 10 more points each round. Clarissa 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 Clarissa has after x rounds. Use the equation to complete the table with the number of points Clarissa 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 Clarissa has after a given number of rounds using the equation \( y = 100 - 5x \), we can substitute \( x \) with the number of rounds.

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 complete the table with the number of points Clarissa has:

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

To address whether they will have the same number of points at some time, we also need to find Jillian's points after each round.

Jillian starts with 10 points and earns 10 more points each round. Her points after \( x \) rounds can be described by the equation: \[ J = 10 + 10x \]

Now we can check for some values of \( x \) to see if there’s a round where Jillian and Clarissa have the same score:

1. For \( x = 4 \): \[ J = 10 + 10(4) = 10 + 40 = 50 \]

2. For \( x = 6 \): \[ J = 10 + 10(6) = 10 + 60 = 70 \]

3. For \( x = 8 \): \[ J = 10 + 10(8) = 10 + 80 = 90 \]

From the calculations:

• At \( x = 4 \), Clarissa has 80 points, Jillian has 50 points (not equal).
• At \( x = 6 \), Clarissa has 70 points, Jillian has 70 points (equal!).
• At \( x = 8 \), Clarissa has 60 points, Jillian has 90 points (not equal).

So, they will have the same number of points after 6 rounds.