Q3 The cost to pick apples at two orchards is shown in an equation and with a description:

Question

Orchard A: y=0.2x+3
Orchard B: Admission is $5 and apples cost $0.75 per pound.
A pound of apples contains about 3 apples. If paying the least amount is most important to you, which orchard should you use if you are going to pick 32 apples? Explain how you arrived at your answer and show your work.

Answer 1

To determine which orchard provides the least cost for picking apples, we need to calculate the total cost for each orchard when picking 32 apples.

Given:

• Orchard A Cost Equation: \( y = 0.2x + 3 \)
  where \( x \) is the number of pounds of apples picked.

• Orchard B Costs:

  • Admission: $5
  • Cost per pound of apples: $0.75
  • 1 pound of apples ≈ 3 apples.

Step 1: Calculate the total weight of apples needed

Since 1 pound contains about 3 apples, to find the total pounds needed for 32 apples, we use the formula:

\[ \text{Pounds of apples} = \frac{\text{Number of apples}}{3} = \frac{32}{3} \approx 10.67 \text{ pounds} \]

Step 2: Calculate the cost for Orchard A

Using the cost equation \( y = 0.2x + 3 \):

Substituting \( x \) with 10.67:

\[ y = 0.2(10.67) + 3 \] \[ y \approx 2.134 + 3 \] \[ y \approx 5.134 \]

So, the total cost at Orchard A is approximately $5.13.

Step 3: Calculate the cost for Orchard B

For Orchard B, we first calculate the cost of the apples after paying the admission fee:

1. Admission cost: $5
2. Cost of apples:
   • Total pounds = 10.67
   • Cost per pound = $0.75

Total cost of apples:

\[ \text{Cost of apples} = 10.67 \times 0.75 = 8.0025 \]

Total cost at Orchard B:

\[ \text{Total cost} = \text{Admission} + \text{Cost of apples} = 5 + 8.0025 = 13.0025 \]

So, the total cost at Orchard B is approximately $13.00.

Conclusion

• Cost at Orchard A: $5.13
• Cost at Orchard B: $13.00

Since the cost at Orchard A is less than the cost at Orchard B, you should pick apples at Orchard A for the least amount of money spent.