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

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?

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.