Question

Impressive imprints sent a brochure with the following table:
Number of shirts:0,5,20,50
Cost:$100,$157.50,$330,$657

How much is the set up charge?_
How much does each shirt cost?_
Write a function that represents the cost of ordering shirts here.___

Answer 1

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:

1. For 0 shirts:
\[
S = 100
\]

2. For 5 shirts:
\[
S + 5C = 157.50
\]

3. For 20 shirts:
\[
S + 20C = 330
\]

4. 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

1. **Setup Charge:** $100
2. **Cost per Shirt:** $11.50
3. **Cost Function:**
\[
\text{Cost}(n) = 100 + 11.50n
\]