Certainly! Let's go through the problem step-by-step to identify the correct equation that models the total cost for picking apples at Wells Orchards.
1. Understand the Components of the Cost:
- There is a fixed entry fee of \$6 to enter the orchard.
- In addition to the entry fee, customers pay \$2 per pound for the apples they pick.
2. Identify the Variables:
- Let \( y \) represent the total cost.
- Let \( x \) represent the number of pounds of apples picked by a customer.
3. Formulate the Total Cost Equation:
- The total cost \( y \) consists of two parts: the fixed entry fee and the variable cost for the apples.
- The fixed entry fee is a constant amount which is \$6.
- The variable cost depends on the number of pounds of apples picked, which is \$2 per pound. Hence, if a customer picks \( x \) pounds of apples, the cost for the apples will be \( 2x \).
4. Combine the Costs:
- Thus, the total cost \( y \) can be expressed as the sum of the entry fee and the variable cost for the apples:
[tex]\[
y = 2x + 6
\][/tex]
5. Verify the Equation with the Given Choices:
- Option A: \( y = 2x + 6 \) (This equation correctly represents the total cost as derived).
- Option B: \( y = 2(x + 6) \) (This incorrectly suggests that the per-pound cost applies to both the apples and the entry fee).
- Option C: \( y = x(6 + 2) \) (This incorrectly multiplies the total of entry fee and per-pound cost by \( x \)).
- Option D: \( y = 6x + 2 \) (This incorrectly suggests a per-pound cost of \[tex]$6 and a fixed cost of \$[/tex]2).
Given the correct formulation and the verification of the choices, the correct answer is:
A. [tex]\( y = 2x + 6 \)[/tex]
