A sponsor of a youth basebail team buys new hats and jerseys for the players on the team. Each hat costs $10 and each jersey costs $20. The eponsor also donates $200 to help pay for umpires. The sponsor spends a total of $650. How many players are on the team?

Let's define the variables:

- Let $ x $ represent the number of players on the team.
- Each player gets a hat and a jersey.

The cost breakdown is as follows:
- Each hat costs $10, so the total cost for hats is $ 10x $.
- Each jersey costs $20, so the total cost for jerseys is $ 20x $.
- The sponsor also donates $200 to help pay for the umpires.

The total amount spent by the sponsor is $650, so we can write the equation:
\[
10x + 20x + 200 = 650
\]

Simplifying the equation:
\[
30x + 200 = 650
\]

Now, subtract 200 from both sides:
\[
30x = 450
\]

Finally, divide both sides by 30:
\[
x = \frac{450}{30} = 15
\]

So, there are 15 players on the team.

Would you like further clarification or more details on this?

Here are five related questions to think about:
1. What if the sponsor donated $300 instead of $200, how many players would be on the team?
2. If the cost of the jersey increased to $25, how would that affect the total cost?
3. How would you write the equation if the hats cost $12 instead of $10?
4. What would happen if there were an additional $100 expense for transportation?
5. How would the total cost change if 5 more players joined the team?

**Tip:** When dealing with cost-related problems, break down each expense category and use variables to set up an equation easily.

A sponsor of a youth baseball team buys new hats and jerseys for the players on the team. Each hat costs $10 and each jersey costs $20. The sponsor also donates $200 to help pay for umpires. The sponsor spends a total of $650. How many players are on the team?

Learn how to solve an algebraic equation involving cost calculation for a youth baseball team. This problem covers concepts like linear equations and basic algebra, suitable for students in Grades 6-8. Find out how many players are on the team based on the sponsor's expenses.

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