Blue's Berry Farm charges Percy a total of 
\[\$24.75\] for entrance and 
\[2.5\] kilograms of strawberries. The entrance fee is 
\[\$6\], and the price for each kilogram of strawberries is constant.
The total cost 
\[C\] for picking strawberries is a function of 
\[x\], the kilograms of strawberries picked.
Write the function's formula.

We are given the following information:

- Entrance fee = \$6
- Percy pays a total of \$24.75, which includes the entrance fee and the cost of 2.5 kilograms of strawberries.
- The price per kilogram of strawberries is constant.

Let $ C(x) $ be the total cost function, where $ x $ is the number of kilograms of strawberries picked. The total cost function $ C(x) $ is the sum of the entrance fee and the cost of the strawberries.

### Step 1: Determine the cost of strawberries per kilogram
The total cost Percy pays is \$24.75. We can calculate the cost of the strawberries alone by subtracting the entrance fee from the total:

\[
\text{Cost of strawberries} = 24.75 - 6 = 18.75
\]

Now, since Percy picked 2.5 kilograms of strawberries, the cost per kilogram $ p $ is:

\[
p = \frac{18.75}{2.5} = 7.50 \, \text{dollars per kilogram}
\]

### Step 2: Write the function formula
The total cost $ C(x) $ is the entrance fee plus the cost of picking $ x $ kilograms of strawberries at a rate of \$7.50 per kilogram:

\[
C(x) = 6 + 7.50x
\]

Thus, the formula for the total cost function is:

\[
C(x) = 6 + 7.50x
\]

### Clarification Questions:
1. Do you need to verify the correctness of the formula with another example?
2. Should we graph this function to better understand it?
3. Would you like help solving for specific values of $ x $?
4. Should we calculate the cost for different amounts of strawberries?
5. Do you need further clarification on how the entrance fee and price per kilogram relate?
6. Would you like to explore the concept of linear functions in more detail?
7. Are there additional conditions or constraints that need to be considered for this function?
8. Do you need help with using this formula in a different scenario?

### Tip:
When creating a function, always ensure to include fixed costs (like entrance fees) separately from variable costs (like cost per kilogram of strawberries) to clearly understand the relationship.

Understand how to calculate the total cost function for picking strawberries at Blue's Berry Farm. Includes a detailed step-by-step solution with examples. Suitable for Grades 7-9 students.

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