Alfonso's chocolate bar  cost PHP 40 per piece. However if you buy more than 10 piece's, there will be a marked down of PHP 30 to it's total price. Use a piecewise function to represent the cost in terms of the number n of chocolate bars brought.

To represent the cost of Alfonso's chocolate bars in terms of the number \( n \) of chocolate bars bought, we can define a piecewise function \( C(n) \). The cost per chocolate bar is PHP 40, and if more than 10 pieces are bought, there's a PHP 30 discount on the total price. The piecewise function can be defined as:

\[
C(n) = \begin{cases} 
40n & \text{if } n \leq 10 \\
40n - 30 & \text{if } n > 10 
\end{cases}
\]

### Explanation:
- **If \( n \leq 10 \):** The total cost is simply \( 40n \), since no discount applies.
- **If \( n > 10 \):** The total cost is \( 40n \) minus the PHP 30 discount.

Would you like more details or have any questions?

### Related Questions:
1. What is the total cost if Alfonso buys 8 chocolate bars?
2. How much does Alfonso save if he buys 12 chocolate bars compared to buying them individually?
3. At what number of chocolate bars does the discount start to apply?
4. How would the piecewise function change if the discount was PHP 50 instead of PHP 30?
5. What would the function look like if the discount applied only when buying exactly 10 bars?

### Tip:
When dealing with piecewise functions, always ensure to clearly define the conditions for each piece to avoid confusion.

Understand how to calculate the cost of Alfonso's chocolate bars based on the number purchased using piecewise functions. Includes scenarios with and without discounts. Suitable for high school students and those interested in applied mathematics.

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