Question

Sophia is in the business of manufacturing phones. She must pay a daily fixed cost of $200 to rent the building and equipment, and also pays a cost of $100 per phone produced for materials and labor. Make a table of values and then write an equation for C, commaC, in terms of p, commap, representing total cost, in dollars, of producing pp phones in a given day.
Your answer has been placed on the table in column 2 row 5 with a green checkmark
Number of Phones Manufactured Total Cost to Manufacture Phones
00 200, check mark200✓200
11 300, check mark300✓300
22 400, check mark400✓400
33 500, check mark500✓500
Answer
Attempt 1 out of 2
The number of attempts on this specific problem before you are marked incorrect

C, equalsC=

Answer 1

To determine the total cost \( C \) in terms of the number of phones produced \( p \), we can start by calculating the total cost based on the fixed costs and variable costs.

1. **Fixed Costs**: This is the amount that Sophia pays daily, regardless of the number of phones produced, which is $200.
2. **Variable Costs**: This is the cost of producing each phone, which is $100 per phone.

The total cost \( C \) can be expressed as:

\[
C = \text{Fixed Cost} + \text{Variable Cost per phone} \times \text{Number of phones produced}
\]

Using the values provided:

\[
C = 200 + 100p
\]

Thus, the equation for total cost \( C \) in terms of the number of phones \( p \) is:

\[
C = 100p + 200
\]

### Table of Values
Here's a breakdown of total costs for different quantities of produced phones:

\[
\begin{array}{|c|c|}
\hline
\text{Number of Phones Manufactured (p)} & \text{Total Cost (C)} \\
\hline
0 & 200 \\
1 & 300 \\
2 & 400 \\
3 & 500 \\
\hline
\end{array}
\]

This table aligns with the values indicated in your question, confirming that the equation \( C = 100p + 200 \) accurately captures the relationship between the number of phones produced \( p \) and the total cost \( C \).