Question

Peanuts sell for $5/lb. Cashews sell for $8/lb. Suppose two pounds of peanuts are mixed with three pounds of cashews.
Find the price per pound of the mixture.

Answer 1

To find the price per pound of the mixture, we first need to calculate the total cost and total weight of the mixture.

1. **Calculate the total cost of the peanuts:**
\[
\text{Cost of peanuts} = \text{Weight of peanuts} \times \text{Price per pound of peanuts}
\]
\[
= 2 \text{ lbs} \times 5 \text{ dollars/lb} = 10 \text{ dollars}
\]

2. **Calculate the total cost of the cashews:**
\[
\text{Cost of cashews} = \text{Weight of cashews} \times \text{Price per pound of cashews}
\]
\[
= 3 \text{ lbs} \times 8 \text{ dollars/lb} = 24 \text{ dollars}
\]

3. **Calculate the total cost of the mixture:**
\[
\text{Total cost} = \text{Cost of peanuts} + \text{Cost of cashews}
\]
\[
= 10 \text{ dollars} + 24 \text{ dollars} = 34 \text{ dollars}
\]

4. **Calculate the total weight of the mixture:**
\[
\text{Total weight} = \text{Weight of peanuts} + \text{Weight of cashews}
\]
\[
= 2 \text{ lbs} + 3 \text{ lbs} = 5 \text{ lbs}
\]

5. **Calculate the price per pound of the mixture:**
\[
\text{Price per pound of mixture} = \frac{\text{Total cost}}{\text{Total weight}}
\]
\[
= \frac{34 \text{ dollars}}{5 \text{ lbs}} = 6.80 \text{ dollars/lb}
\]

Therefore, the price per pound of the mixture is **$6.80**.