Question

which expression could brennan use to calculate the approximate costs for purchasing and operating taps in the first season?

\\(\boldsymbol{\frac{\text{initial equipment costs per tap}}{\text{number of trees tapped}}}\\)

\\(\boldsymbol{\text{number of trees tapped} \times \text{initial equipment costs per tap}}\\)

\\(\boldsymbol{\frac{\text{initial equipment costs per tap} + \text{yearly operating cost per tap}}{\text{number of trees tapped}}}\\)

\\(\boldsymbol{\text{number of trees tapped} \times (\text{yearly operating cost per tap} + \text{initial equipment costs per tap})}\\)

Explanation:

To calculate the total cost for purchasing and operating taps in the first season, we need to consider both the initial equipment cost and the operating cost for each tap, multiplied by the number of trees tapped (since each tree has a tap).

Step 1: Analyze each option

• Option 1: Dividing initial cost per tap by number of trees tapped would give a cost per tree, not total cost.
• Option 2: Only considers initial equipment cost, not operating cost.
• Option 3: Dividing the sum of costs by number of trees tapped gives a cost per tree, not total cost.
• Option 4: The total cost per tap is initial equipment cost per tap plus yearly operating cost per tap. Multiplying this by the number of trees tapped (which is the number of taps, assuming one tap per tree) gives the total cost for all taps.

Answer:

D. number of trees tapped × (yearly operating cost per tap + initial equipment costs per tap)