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The graph visually confirms our calculation: Trevor and his cousin's scores will be tied at 60 points each after 4 turns.

Would you like any further details or have any questions about this problem?

Here are some related questions you might consider:
1. What would happen if the point values for the colored sticks were changed?
2. How many turns would it take for the cousin to surpass Trevor if the game continued beyond the tie?
3. What would be the score difference after 10 turns?
4. Can you determine a general formula to calculate the number of turns needed for a tie if the initial scores or points per turn are different?
5. What strategies could Trevor adopt to maintain his lead?

**Tip:** When setting up equations based on a word problem, it helps to first define your variables clearly and then translate each statement into a mathematical expression step by step. This ensures accuracy in your setup and helps avoid common errors.

Trevor and his cousin are playing a game where they pick up coloured sticks. Trevor currently has 40 points and likes to pick up the teal sticks, earning 5 points every turn. His cousin just lost all his points on the previous turn, and has a strategy to catch up by getting all the pink ones, earning 15 points per turn. In a certain number of turns, the score will be tied. How long will that take?

In this problem, Trevor has 40 points and earns 5 points per turn, while his cousin earns 15 points per turn from 0 points. Find out how many turns it will take for their scores to be tied by solving simultaneous linear equations and graphing the results. Perfect for Grades 7-10.

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