A certain noodles costs Php 50.00 per order. However, the owner decided to give discount if you purchased 10 orders or more. Create a function (n) which represent the total cost of the noodles n that you will be purchased.

To represent the total cost \( C(n) \) of the noodles as a function of \( n \), where \( n \) is the number of orders, we can define the function with two cases:

1. If you purchase fewer than 10 orders (i.e., \( n < 10 \)), the cost is simply \( 50 \times n \).
2. If you purchase 10 or more orders (i.e., \( n \geq 10 \)), you will receive a discount. Let's assume the discounted price is \( d \) per order.

The function \( C(n) \) can be written as:

\[
C(n) = 
\begin{cases} 
50n & \text{if } n < 10 \\
d \times n & \text{if } n \geq 10 
\end{cases}
\]

If the discount is specified (for example, 10% off), you can adjust the value of \( d \) accordingly. For example, if the discount is 10%, \( d \) would be \( 50 \times 0.9 = 45 \) Php per order.

So, if the discount is 10%, the function becomes:

\[
C(n) = 
\begin{cases} 
50n & \text{if } n < 10 \\
45n & \text{if } n \geq 10 
\end{cases}
\]

Would you like to specify a discount amount or rate, or do you have any questions? 

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Here are 5 related questions to consider:

1. What if the discount applies only after purchasing 20 orders?
2. How would the function change if the discount applied progressively (e.g., 10% for 10-19 orders, 20% for 20+ orders)?
3. What would be the total cost for exactly 10 orders?
4. How would the function change if there was a fixed discount (e.g., Php 50 off for 10 or more orders)?
5. How does this function change if the price per order increases for every 5 orders?

**Tip:** When defining piecewise functions, clearly distinguish between different cases using inequalities, ensuring that all possible scenarios are covered.

Learn how to calculate the total cost of noodles based on the number of orders, incorporating discounts for purchases of 10 or more orders. This problem involves piecewise functions and discount calculations, suitable for high school students.

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