Kara's Custom Tees experienced fixed costs of ​$500 and variable costs of ​$4 a shirt. Write an equation that can be used to determine the total expenses encountered by​ Kara's Custom Tees. Let x be the number of​ shirts, and let​ C(x) be the total cost of producing x shirts.​ Then, calculate the cost of producing 5 shirts.
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Part 1
An equation that can be used to determine the total cost of producing x shirts is ​C(x)equals
  
enter your response here.

The total cost $ C(x) $ is composed of two parts: fixed costs and variable costs.

1. The fixed cost is $500, which remains the same regardless of how many shirts are produced.
2. The variable cost is $4 per shirt, which depends on the number of shirts produced.

Therefore, the total cost equation can be written as:

\[
C(x) = 500 + 4x
\]

where $ x $ is the number of shirts produced, and $ C(x) $ is the total cost.

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### Now, let's calculate the cost of producing 5 shirts:

Substitute $ x = 5 $ into the equation:

\[
C(5) = 500 + 4(5) = 500 + 20 = 520
\]

So, the total cost of producing 5 shirts is **$520**.

Would you like further clarification or more details on this?

Here are 5 questions to further explore:
1. What happens to the total cost as the number of shirts increases?
2. How would the equation change if the fixed costs increased to $600?
3. How does the variable cost affect the overall cost when producing large quantities of shirts?
4. What would the total cost be if no shirts were produced?
5. Can you express the variable cost as a percentage of the total cost?

**Tip:** When solving problems involving fixed and variable costs, it’s useful to separate them to understand how each part contributes to the total.

Kara's Custom Tees experienced fixed costs of $500 and variable costs of $4 a shirt. Write an equation that can be used to determine the total expenses encountered by Kara's Custom Tees. Let x be the number of shirts, and let C(x) be the total cost of producing x shirts. Then, calculate the cost of producing 5 shirts.

Learn how to calculate the total cost of producing shirts for Kara's Custom Tees. The problem involves a fixed cost of $500 and a variable cost of $4 per shirt, leading to the equation C(x) = 500 + 4x. Discover how to solve this equation and calculate the cost for any number of shirts, such as 5 shirts costing $520. This problem is ideal for students in Grades 6-8 learning about linear equations.

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