Nut Mix Michael and Kevin return to the candy store, but this time they want to purchase nuts. They can’t decide among peanuts, cashews, or almonds. They again agree to create a mix. They bought 2.5 pounds of peanuts for \$1.30 per pound, 4 pounds of cashews for \$4.50 per pound, and 2 pounds of almonds for \$3.75 per pound. Determine the price per pound of the mix.

Verified step by step guidance

1. Calculate the total cost of each type of nut by multiplying the weight by the price per pound. For peanuts, use the formula: \(\text{Cost}_{\text{peanuts}} = 2.5 \times 1.30\).
2. Similarly, calculate the total cost for cashews: \(\text{Cost}_{\text{cashews}} = 4 \times 4.50\), and for almonds: \(\text{Cost}_{\text{almonds}} = 2 \times 3.75\).
3. Add the total costs of all three types of nuts to find the total cost of the mix: \(\text{Total Cost} = \text{Cost}_{\text{peanuts}} + \text{Cost}_{\text{cashews}} + \text{Cost}_{\text{almonds}}\).
4. Add the weights of all the nuts to find the total weight of the mix: \(\text{Total Weight} = 2.5 + 4 + 2\).
5. Divide the total cost by the total weight to find the price per pound of the mix: \(\text{Price per pound} = \frac{\text{Total Cost}}{\text{Total Weight}}\).

Key Concepts

Weighted Average

A weighted average calculates the mean of values that contribute unequally to the total. In this problem, the price per pound of the nut mix depends on the cost and weight of each type of nut, so each price is weighted by its corresponding weight before averaging.

Total Cost Calculation

To find the overall cost of the nut mix, multiply the price per pound of each nut by its weight, then sum these amounts. This total cost is essential for determining the average price per pound of the combined mixture.

Price per Pound of Mixture

The price per pound of the nut mix is found by dividing the total cost of all nuts by the total weight of the mixture. This gives a single price that reflects the combined cost per unit weight of the mixed nuts.