To determine the total cost, [tex]\( y \)[/tex], for [tex]\( x \)[/tex] pounds of pumpkins, we need to consider both the entry fee and the cost per pound of pumpkins.
1. Entry Fee: Every customer must pay a fixed entry fee of \[tex]$4 immediately upon entering the patch.
2. Cost per Pound: Each customer also pays \$[/tex]3 for every pound of pumpkins they pick. If a customer picks [tex]\( x \)[/tex] pounds of pumpkins, the cost for the pumpkins is [tex]\( 3 \cdot x \)[/tex].
Now, let's combine these two components:
- The total cost [tex]\( y \)[/tex] will consist of the fixed entry fee added to the cost for the pounds of pumpkins:
[tex]$ y = \text{entry fee} + \text{(cost per pound)} \cdot x $[/tex]
Substituting the given values, we have:
- Entry Fee = \[tex]$4
- Cost per Pound = \$[/tex]3
- Number of Pounds = [tex]\( x \)[/tex]
Therefore,
[tex]$ y = 4 + 3x $[/tex]
To match this step-by-step model with the given answer choices, convert it into the standard form:
- [tex]\( y = 3x + 4 \)[/tex]
Thus, the correct equation that models the total cost [tex]\( y \)[/tex] for [tex]\( x \)[/tex] pounds of pumpkins is:
D. [tex]\( y = 3x + 4 \)[/tex]
