Fernando purchased 1 pound of dried cranberries and 4 pounds of almonds to make a trail mix. Cranberries cost $[tex]$4[/tex] per pound, and almonds cost $[tex]$5[/tex] per pound. What is the price per pound of the trail mix? $ $\square$
Answer (1)
Calculate the total cost of cranberries: 1 × $4 = $4 .
Calculate the total cost of almonds: 4 × $5 = $20 .
Calculate the total weight of the mixture: 1 + 4 = 5 pounds.
Calculate the price per pound of the mixture: 5 $24 = $4.80 .
Explanation
Understanding the Problem Fernando is making a trail mix with cranberries and almonds. We need to find the price per pound of the final mixture. We know the weight and price per pound of the cranberries and almonds.
Cost of Cranberries First, let's calculate the total cost of the cranberries. Fernando bought 1 pound of cranberries at $4 per pound. So, the total cost of cranberries is: 1 pound × $4 per pound = $4
Cost of Almonds Next, let's calculate the total cost of the almonds. Fernando bought 4 pounds of almonds at $5 per pound. So, the total cost of almonds is: 4 pounds × $5 per pound = $20
Total Cost of Mixture Now, let's find the total cost of the mixture by adding the cost of cranberries and the cost of almonds: $4 + $20 = $24
Total Weight of Mixture Next, we need to find the total weight of the mixture. Fernando used 1 pound of cranberries and 4 pounds of almonds. So, the total weight of the mixture is: 1 pound + 4 pounds = 5 pounds
Price per Pound of Mixture Finally, we can calculate the price per pound of the trail mix by dividing the total cost of the mixture by the total weight of the mixture: Price per pound = Total weight Total cost = 5 pounds $24 = $4.80 per pound
Final Answer Therefore, the price per pound of the trail mix is $4.80.
Examples
When creating a product that combines different ingredients, like a smoothie or a cleaning solution, calculating the cost per unit (like per pound or per liter) is essential for pricing and profitability. This problem demonstrates how to calculate the weighted average cost, which is a fundamental concept in business and finance. For example, a bakery might use this calculation to determine the cost per loaf of bread made from different types of flour with varying prices. By understanding the cost per unit, businesses can make informed decisions about pricing, production, and ingredient sourcing to maximize their profits.
