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Let's analyze the problem to complete the table and form the equation for the total cost $ C $ in terms of $ p $, where $ p $ represents the number of phones manufactured.

### Given Information:
1. **Fixed cost:** $400 (this is incurred regardless of the number of phones produced).
2. **Variable cost per phone:** $125 per phone (for materials and labor).

### Step-by-Step Solution:

The **total cost $ C $** of producing $ p $ phones can be represented as:
\[
C = 400 + 125p
\]
where:
- $ 400 $ is the fixed cost.
- $ 125p $ is the cost per phone multiplied by the number of phones produced, $ p $.

### Filling in the Table

Now, we calculate the total cost for each given number of phones:

1. **When $ p = 0 $:**
   \[
   C = 400 + 125 \times 0 = 400
   \]
   
2. **When $ p = 1 $:**
   \[
   C = 400 + 125 \times 1 = 525
   \]
   
3. **When $ p = 2 $:**
   \[
   C = 400 + 125 \times 2 = 650
   \]
   
4. **When $ p = 3 $:**
   \[
   C = 400 + 125 \times 3 = 775
   \]

### Completed Table

| Number of Phones Manufactured ($ p $) | Total Cost to Manufacture Phones ($ C $) |
|-----------------------------------------|---------------------------------------------|
| 0                                       | 400                                         |
| 1                                       | 525                                         |
| 2                                       | 650                                         |
| 3                                       | 775                                         |

### Final Equation
The equation for the total cost $ C $ in terms of $ p $ is:
\[
C = 400 + 125p
\]

Would you like further explanation on any step, or do you have questions about how to interpret this equation?

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Here are 5 related questions to expand on this topic:
1. What would be the total cost if 10 phones were manufactured?
2. How would the equation change if the fixed cost increased to $500?
3. What is the cost per phone produced after accounting for the fixed cost?
4. How many phones would Madison need to produce to reach a total cost of $1,000?
5. If the variable cost per phone changed to $150, what would the new equation for $ C $ be?

**Tip:** In word problems involving costs, separating fixed and variable costs helps you create accurate cost equations.

Madison is in the business of manufacturing phones. She must pay a daily fixed cost of $400 to rent the building and equipment, and also pays a cost of $125 per phone produced for materials and labor. Make a table of values and then write an equation for C, in terms of p, representing total cost, in dollars, of producing p phones in a given day.

Explore how to calculate the total cost of manufacturing phones with a fixed daily cost of $400 and an additional cost of $125 per phone produced. Learn to create a table of values and derive a linear equation to represent total cost in terms of the number of phones manufactured. Ideal for middle school students in Grades 6-8.

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