Let's analyze the question and find the correct formula to represent the total cost, [tex]\( y \)[/tex], for [tex]\( x \)[/tex] pounds of apples at Wells Orchard.
1. Fixed Cost (Park Access Fee): Every customer must pay a flat fee of \[tex]$6 for park access, regardless of the amount of apples picked.
2. Variable Cost (Cost per Pound of Apples): In addition to the fixed park access fee, customers must also pay \$[/tex]2 per pound of apples they pick.
To find the total cost [tex]\( y \)[/tex], we need to combine these two costs (fixed and variable):
### Step-by-Step Solution:
1. Identify the fixed cost:
- The fixed cost for park access is \[tex]$6.
2. Identify the variable cost:
- The cost per pound of apples is \$[/tex]2.
- If [tex]\( x \)[/tex] represents the number of pounds of apples, then the total variable cost for the apples is [tex]\( 2x \)[/tex] dollars.
3. Combine the costs:
- The total cost [tex]\( y \)[/tex] is the sum of the fixed cost (park access fee) and the variable cost (cost for the number of pounds of apples picked).
[tex]\[ y = 2x + 6 \][/tex]
Now, let's match this derived equation with the given options:
A. [tex]\( y = 2x + 6 \)[/tex] [tex]\(\leftarrow \text{Correct answer} \)[/tex]
B. [tex]\( y = x(6 + 2) \)[/tex]
- This simplifies to [tex]\( y = 8x \)[/tex], which is incorrect because it doesn't account correctly for the flat fee and the cost per pound correctly.
C. [tex]\( y = 6x + 2 \)[/tex]
- This implies that the cost per pound is \[tex]$6 and the fixed fee is \$[/tex]2, which is incorrect based on the given information.
D. [tex]\( y = 2(x + 6) \)[/tex]
- This simplifies to [tex]\( y = 2x + 12 \)[/tex], which is also incorrect as it misrepresents the additional fixed fee.
Thus, the correct option is:
A. [tex]\( y = 2x + 6 \)[/tex]
