Yolanda wishes to develop a new type of meatloaf to sell at her restaurant. She decides to combine 2 pounds of ground sirloin (cost \$2.70 per pound), 1 pound of ground turkey (cost \$1.30 per pound), and 12\frac{1}{2}21 pound of ground pork (cost \$1.80 per pound). What is the cost per pound of the meatloaf?

Verified step by step guidance

1. First, identify the weight and cost per pound of each type of meat: 2 pounds of ground sirloin at \$2.70 per pound, 1 pound of ground turkey at \$1.30 per pound, and 1.5 pounds (since 12\frac{1}{2}21 is interpreted as 1\frac{1}{2} or 1.5 pounds) of ground pork at \$1.80 per pound.
2. Calculate the total weight of the meatloaf by adding the weights of all the meats: \$2 + 1 + 1.5$ pounds.
3. Calculate the total cost for each type of meat by multiplying the weight by the cost per pound: for sirloin, \$2 \times 2.70\(; for turkey, \)1 \times 1.30\(; and for pork, \)1.5 \times 1.80$.
4. Add the total costs of all the meats to find the overall cost of the meatloaf.
5. Finally, find the cost per pound of the meatloaf by dividing the total cost by the total weight: \(\text{Cost per pound} = \frac{\text{Total cost}}{\text{Total weight}}\).

Key Concepts

Weighted Average Cost

Weighted average cost calculates the overall cost per unit when combining items with different costs and quantities. It is found by multiplying each item's cost by its quantity, summing these products, and dividing by the total quantity. This concept helps determine the average price per pound of the combined meatloaf.

Unit Cost

Unit cost refers to the cost per single unit of measure, such as per pound in this problem. Understanding unit cost allows comparison and combination of different ingredients priced differently, facilitating the calculation of total and average costs.

Fractional Quantities

Fractional quantities involve parts of a whole unit, such as 1.5 pounds of meat. Properly handling fractions or decimals in quantities is essential for accurate calculations of total weight and cost in mixture problems.