To determine which orchard is cheaper for picking 32 apples, we will calculate the total cost of picking apples at both Orchard A and Orchard B. We need to convert the number of apples into pounds, since the price for Orchard B is given in pounds.
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Convert Apples to Pounds: \[ 1 \text{ pound of apples} \approx 3 \text{ apples} \] Therefore, to find the number of pounds for 32 apples: \[ \text{Pounds of apples} = \frac{32 \text{ apples}}{3 \text{ apples/pound}} \approx 10.67 \text{ pounds} \]
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Calculate the Cost at Orchard A: The cost equation for Orchard A is given as: \[ y = 0.2x + 3 \] Here, \(x\) represents the number of pounds, which we will substitute: \[ y = 0.2(10.67) + 3 \] First, calculate \(0.2 \times 10.67\): \[ 0.2 \times 10.67 = 2.134 \] Now substitute this into the equation: \[ y = 2.134 + 3 = 5.134 \]
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Calculate the Cost at Orchard B: At Orchard B, there is an admission of $5 plus the cost of apples at $0.75 per pound: \[ \text{Total cost} = \text{Admission} + (\text{Cost per pound} \times \text{Pounds}) \] Substituting the values: \[ \text{Total cost} = 5 + (0.75 \times 10.67) \] First, calculate \(0.75 \times 10.67\): \[ 0.75 \times 10.67 \approx 8.0025 \] Now substitute back: \[ \text{Total cost} = 5 + 8.0025 \approx 13.0025 \]
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Compare Costs:
- Cost at Orchard A: $5.134
- Cost at Orchard B: $13.0025
Since $5.134 < $13.0025, Orchard A is the cheaper option for picking 32 apples.
Conclusion: If you are looking for the least amount to spend, you should choose Orchard A, which will cost you approximately $5.13 compared to $13.00 at Orchard B.