2 bags of sugar at Nx per bag are mixed with 3 bags of sugar at Ny per bag. What is the cost in N of the mixture per bag?

Analyze the question: Two lots of sugar with different prices per bag are mixed. We need the cost per bag of the mixture, which is the average cost.

Concept: Cost per bag of a mixture = (total cost of all bags) ÷ (total number of bags)

Solution:

• 2 bags at Nx each: cost = 2x
• 3 bags at Ny each: cost = 3y
• Total cost = 2x + 3y
• Total number of bags = 2 + 3 = 5

Cost per bag of the mixture:

Checking the options:

• A. (2x + 3y)/5 matches our result.
• B. (x + y)/2 ignores the number of bags of each type.
• C. x/2 + y/3 divides the prices by the numbers of bags, which is wrong.
• D. (x + y)/5 does not multiply each price by its number of bags.
• E. (3x + 2y)/5 swaps the quantities (it would be correct for 3 bags at x and 2 bags at y).

Tip: For mixture questions, always weight each price by its quantity: (quantity₁ × price₁ + quantity₂ × price₂) ÷ total quantity. Make sure each quantity multiplies its own price, because option E is a common trap that swaps them.