To determine which equation correctly represents the transport cost for every 50 pounds of cold cuts transported, we need to analyze the given cost structure:
1. Fixed Cost: It costs [tex]$1,200 to rent the truck. This fixed cost does not change regardless of the weight transported.
2. Variable Cost: It costs an additional $[/tex]100 for every 50 pounds transported. This cost changes based on the weight being transported.
Let's define the variables:
- Let [tex]\( x \)[/tex] represent the number of units of 50 pounds transported.
- Let [tex]\( y \)[/tex] represent the total transport cost.
Given these definitions:
- The fixed cost [tex]\( \$1,200 \)[/tex] is constant.
- The variable cost is [tex]\( \$100 \)[/tex] per unit of 50 pounds, so the number of units [tex]\( x \)[/tex] will determine this additional cost component.
To generate the total cost [tex]\( y \)[/tex], we combine the fixed cost and the variable cost:
[tex]\[ y = 1200 + (100 \times x) \][/tex]
Therefore, the correct equation that represents the transport cost [tex]\( y \)[/tex] for every [tex]\( x \)[/tex] units of 50 pounds of cold cuts transported is:
[tex]\[ y = 1200 + 100x \][/tex]
Upon evaluating the given multiple-choice options:
A. [tex]\( y = 1200 - 100x \)[/tex] — This option incorrectly subtracts the variable cost, which is not correct.
B. [tex]\( y = 1200 + 100x \)[/tex] — This option correctly adds the variable cost to the fixed cost, aligning with our equation.
C. [tex]\( y = 1200x + 100 \)[/tex] — This option inaccurately multiplies the fixed cost by [tex]\( x \)[/tex] and adds a constant, which is incorrect.
D. [tex]\( y = 100x - 1200 \)[/tex] — This option incorrectly subtracts the fixed cost, which is not correct.
The correct answer is:
[tex]\[ \boxed{B} \][/tex]
