Question

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.
\[C=\]

Answer 1

To find the total cost \( C \) as a function of \( x \) (the kilograms of strawberries picked), we first need to analyze the provided information.

1. The entrance fee is a constant \( \$6 \).
2. The total payment made by Percy is \( \$24.75 \).
3. From this total payment, we can find out how much was spent on strawberries.

Let \( p \) be the price per kilogram of strawberries. Since Percy bought \( 2.5 \) kilograms, the cost for the strawberries is:

\[
\text{Cost of strawberries} = 2.5 \times p
\]

Now, we can express the total cost \( C \) as the sum of the entrance fee and the cost of strawberries:

\[
C = \text{Entrance fee} + \text{Cost of strawberries}
\]

Substituting the known values:

\[
C = 6 + 2.5p
\]

Now, we also know that the total cost (\( C \)) that Percy paid is \( 24.75 \):

\[
C = 24.75 = 6 + 2.5p
\]

To find \( p \), we solve for it:

\[
24.75 - 6 = 2.5p
\]
\[
18.75 = 2.5p
\]
\[
p = \frac{18.75}{2.5} = 7.5
\]

Now, would replace \( p \) in the total cost function:

We can express \( C \) as a function of \( x \) where \( x \) is the kilograms of strawberries picked:

\[
C = 6 + 7.5x
\]

Thus, the required function for the total cost \( C \), in terms of the kilograms \( x \), is:

\[
C = 6 + 7.5x
\]