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Let's go through the questions one by one and solve them based on the given information.

Mariel has a cellphone plan with:
- A monthly fee of ₱2,500.00
- 240 minutes of call included
- ₱7.50 charged for each additional minute of usage

**6. Which of the following pertains to the monthly cost function?**

Let's derive the monthly cost function, \( C(x) \):
- If \( x \) is the number of minutes used in a month.
- The base cost is ₱2,500.
- Additional cost for \( x \) minutes beyond the included 240 minutes is \( 7.50(x - 240) \).

So, the cost function should be:
\[ C(x) = 2500 + 7.50(x - 240) \]
\[ C(x) = 2500 + 7.50x - 1800 \]
\[ C(x) = 700 + 7.50x \]

This matches with option (c).

**Answer: c. \( C(x) = 700 + 7.50x \)**

**7. What value of \( x \) will not require any additional charge in her monthly bill?**

Since 240 minutes are included in the plan without any additional charge, \( x \) should be less than or equal to 240.

**Answer: d. \( x \leq 240 \)**

**8. How many additional minutes of call did she make, if she paid ₱2,800.00 in her monthly bill?**

Let's use the cost function:
\[ 2800 = 700 + 7.50x \]
\[ 2100 = 7.50x \]
\[ x = 280 \]

She used 280 minutes, which is 40 minutes more than the included 240 minutes.

**Answer: b. 40 minutes**

**9. How much is her monthly cost incurred if she made an additional usage of 20 minutes of call?**

Additional minutes = 20
\[ C(260) = 700 + 7.50 \times 260 \]
\[ C(260) = 700 + 1950 \]
\[ C(260) = 2650 \]

**Answer: c. ₱2,650.00**

**10. How much will she need to pay from using a total of 350 minutes of call in one month?**

\[ C(350) = 700 + 7.50 \times 350 \]
\[ C(350) = 700 + 2625 \]
\[ C(350) = 3325 \]

**Answer: c. ₱3,325.00**

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Would you like more details or have any questions?

Here are five related questions to expand your understanding:

1. How would the cost function change if the monthly fee increased to ₱3,000?
2. If Mariel used 500 minutes in a month, what would be her total bill?
3. How many additional minutes can Mariel use if she wants to keep her bill below ₱3,000?
4. If the additional minute charge was reduced to ₱5.00, what would be the new cost function?
5. How much would Mariel save if the plan offered 300 free minutes instead of 240?

**Tip:** Always ensure you understand how to derive the cost function based on the given pricing structure to solve these types of problems efficiently.

Mariel wanted to avail a cellphone plan that offers a monthly fee of ₱2,500.00. It includes 240 minutes of call and charges ₱7.50 for each additional minute of usage.

Learn how to calculate the monthly cost of a cellphone plan with a base fee of ₱2,500, 240 free minutes, and additional charges of ₱7.50 per minute. This problem covers linear equations and cost functions for Grades 10-12.

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