The cost to pick apples at two orchards is shown in an equation and with a description, where x represents the number of apples:

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.

(2 points)

Answer 1

To determine which orchard offers the better deal for picking 32 apples, we’ll need to calculate the total cost for each orchard.

Orchard A

The cost equation is given by: \[ y = 0.2x + 3 \] Where \( y \) is the total cost and \( x \) is the number of apples.

If we substitute 32 apples for \( x \): \[ y = 0.2(32) + 3 \] \[ y = 6.4 + 3 \] \[ y = 9.4 \]

So, the total cost at Orchard A is $9.40.

Orchard B

At Orchard B, there is an admission fee of $5, and apples cost $0.75 per pound. Since a pound contains about 3 apples, we need to find out how many pounds correspond to 32 apples.

First, calculate the number of pounds of apples: \[ \text{Number of pounds} = \frac{32 \text{ apples}}{3 \text{ apples/pound}} \approx 10.67 \text{ pounds} \]

Now calculate the cost of the apples: \[ \text{Cost of apples} = 10.67 \text{ pounds} \times 0.75 \text{ dollars/pound} \approx 8.00 \text{ dollars} \]

Now add the admission fee: \[ \text{Total cost} = 5 + 8.00 = 13.00 \]

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

Conclusion

• The total cost at Orchard A is $9.40.
• The total cost at Orchard B is $13.00.

Since Orchard A costs less than Orchard B for picking 32 apples, you should choose Orchard A to minimize your expenses.