To determine the appropriate equation to model the total cost [tex]\( y \)[/tex] for [tex]\( x \)[/tex] pounds of cherries at Cherry Hill Farm, we need to account for two components: the entrance fee and the cost per pound of cherries.
1. Entrance Fee: Every customer has to pay a fixed fee of \[tex]$4 to enter the farm, regardless of how much cherries they pick. This is a constant amount added to the total cost.
2. Cost Per Pound of Cherries: Customers pay \$[/tex]3.50 per pound for the cherries they pick. Therefore, if a customer picks [tex]\( x \)[/tex] pounds of cherries, the total cost for the cherries alone would be [tex]\( 3.5x \)[/tex].
Combining these two components, the total cost [tex]\( y \)[/tex] can be expressed as the sum of the entrance fee and the variable cost (dependent on the weight of cherries picked).
Thus, the equation for the total cost [tex]\( y \)[/tex] is:
[tex]\[ y = 3.5x + 4 \][/tex]
Let's check the given options to see which one matches this equation:
A. [tex]\( y = 4x + 3.5 \)[/tex]
This suggests a total entrance fee that is dependent on the number of pounds picked, which is incorrect. Thus, option A is not correct.
B. [tex]\( y = x(3.5 + 4) \)[/tex]
This simplifies to [tex]\( y = 3.5x + 4x \)[/tex], which equals [tex]\( y = 7.5x \)[/tex]. This doesn't include the correct fixed entrance fee structure we observed. Therefore, option B is incorrect.
C. [tex]\( y = 3.5x + 4 \)[/tex]
This correctly represents the total cost as the sum of a constant entrance fee of \[tex]$4 and a cost of \$[/tex]3.50 per pound for [tex]\( x \)[/tex] pounds of cherries. Option C is correct.
D. [tex]\( y = 3.5(x + 4) \)[/tex]
This would distribute to [tex]\( y = 3.5x + 14 \)[/tex], which inaccurately suggests the entrance fee is influenced by the pounds of cherries picked. Option D is incorrect.
Therefore, the correct equation is given by:
[tex]\[ y = 3.5x + 4 \][/tex]
As per the choices provided, the answer is:
C. [tex]\( y = 3.5x + 4 \)[/tex]
