Complete the table below:

Mark started selling snacks in the nearby school. In one day, he spends Php200 for rent and Php25 for each snack item he prepares. His expenses in a single day can be expresses as the function C(x) = 25x + 200, where x is the number of items and the C(x) is his daily expenses in pesos. Find his expenses per number of snack items.

No. of snacks

85

100

112

127

139

150

Expenses

G

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To find Mark's daily expenses for each number of snack items, we'll use the function given: 

\[
C(x) = 25x + 200
\]

Here, \( x \) is the number of snack items, and \( C(x) \) represents the total daily expenses in pesos.

Let's calculate the expenses for each number of snack items listed in the table.

1. **For 85 snacks**:
   \[
   C(85) = 25(85) + 200 = 2125 + 200 = 2325 \text{ pesos}
   \]

2. **For 100 snacks**:
   \[
   C(100) = 25(100) + 200 = 2500 + 200 = 2700 \text{ pesos}
   \]

3. **For 112 snacks**:
   \[
   C(112) = 25(112) + 200 = 2800 + 200 = 3000 \text{ pesos}
   \]

4. **For 127 snacks**:
   \[
   C(127) = 25(127) + 200 = 3175 + 200 = 3375 \text{ pesos}
   \]

5. **For 139 snacks**:
   \[
   C(139) = 25(139) + 200 = 3475 + 200 = 3675 \text{ pesos}
   \]

6. **For 150 snacks**:
   \[
   C(150) = 25(150) + 200 = 3750 + 200 = 3950 \text{ pesos}
   \]

### Completed Table:

| No. of snacks | Expenses (Php) |
|---------------|----------------|
| 85            | 2325           |
| 100           | 2700           |
| 112           | 3000           |
| 127           | 3375           |
| 139           | 3675           |
| 150           | 3950           |

Would you like to explore more details, or do you have any other questions?

Here are some related questions you might consider:

1. What would Mark's expenses be if he prepared 200 snacks?
2. How would the total cost function change if the rent increased to Php300?
3. If Mark wants to limit his expenses to Php3500, what is the maximum number of snacks he can prepare?
4. How would the cost per snack item change if he used cheaper ingredients?
5. If Mark increased the price per snack item to Php30, how would that affect his cost function?
6. How much does Mark need to charge per snack to break even if he prepares 150 snacks?
7. What if Mark gets a discount of Php50 on rent, how would the expenses be affected?
8. How do Mark’s expenses change if he prepares 10 more snacks each day?

**Tip:** When analyzing cost functions, always consider both fixed costs (like rent) and variable costs (like materials per item) to understand the overall expense!

Discover how to calculate Mark's daily expenses based on the number of snack items he prepares. Use the cost function C(x) = 25x + 200 to find expenses for different quantities of snacks. Suitable for Grades 9-12.

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