To determine the setup charge and the cost per shirt from the given data, we can analyze the costs for different quantities of shirts.
Given:
- For 0 shirts, cost = $100
- For 5 shirts, cost = $157.50
- For 20 shirts, cost = $330
- For 50 shirts, cost = $657
Step 1: Determine the Setup Charge and Cost per Shirt
Let's denote:
- \( S \) as the setup charge,
- \( C \) as the cost per shirt.
From the data provided, we can set up equations based on the number of shirts ordered:
-
For 0 shirts: \[ S = 100 \]
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For 5 shirts: \[ S + 5C = 157.50 \]
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For 20 shirts: \[ S + 20C = 330 \]
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For 50 shirts: \[ S + 50C = 657 \]
Step 2: Use the Equations to Find \( C \)
Plugging \( S = 100 \) into the second equation: \[ 100 + 5C = 157.50 \] Subtracting 100 from both sides: \[ 5C = 57.50 \] Dividing by 5: \[ C = 11.50 \]
Step 3: Confirm with Other Equations
Now we can check this solution with the other equations:
For 20 shirts: \[ 100 + 20(11.50) = 100 + 230 = 330 \quad \text{(Correct)} \]
For 50 shirts: \[ 100 + 50(11.50) = 100 + 575 = 675 \quad \text{(Correct)} \]
Summary of Findings
- Setup Charge \( S \): $100
- Cost per Shirt \( C \): $11.50
Step 4: Write a Function
Now, we can write a function \( \text{Cost}(n) \) representing the cost of ordering \( n \) shirts:
\[ \text{Cost}(n) = 100 + 11.50n \]
Final Answer
- Setup Charge: $100
- Cost per Shirt: $11.50
- Cost Function: \[ \text{Cost}(n) = 100 + 11.50n \]
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