A mixture consists of 10 L at $2/L and 20 L at $3/L. What is the average cost per liter of the mixture?

A mixture consists of 10 L at $2/L and 20 L at $3/L. What is the average cost per liter of the mixture?

• A. $2.50/L
• B. $2.67/L
• C. $2.75/L
• D. $2.33/L

Answer: (B)

To determine the average cost per liter of the mixture, we first calculate the total cost of each component of the mixture. For the first part of the mixture: - Volume: 10 liters - Cost per liter: $2 - Total cost: \( 10 \, \text{L} \times 2 \, \frac{\text{dollars}}{\text{L}} = 20 \, \text{dollars} \) For the second part of the mixture: - Volume: 20 liters - Cost per liter: $3 - Total cost: \( 20 \, \text{L} \times 3 \, \frac{\text{dollars}}{\text{L}} = 60 \, \text{dollars} \) Next, we combine the total costs of both parts: - Total cost of the mixture: \( 20 \, \text{dollars} + 60 \, \text{dollars} = 80 \, \text{dollars} \) Now, we find the total volume of the mixture: - Total volume: \( 10 \, \text{L} + 20 \, \text{L}

To determine the average cost per liter of the mixture, we first calculate the total cost of each component of the mixture.

For the first part of the mixture:

• Volume: 10 liters

• Cost per liter: $2

• Total cost: ( 10 , \text{L} \times 2 , \frac{\text{dollars}}{\text{L}} = 20 , \text{dollars} )

For the second part of the mixture:

• Volume: 20 liters

• Cost per liter: $3

• Total cost: ( 20 , \text{L} \times 3 , \frac{\text{dollars}}{\text{L}} = 60 , \text{dollars} )

Next, we combine the total costs of both parts:

• Total cost of the mixture: ( 20 , \text{dollars} + 60 , \text{dollars} = 80 , \text{dollars} )

Now, we find the total volume of the mixture:

• Total volume: ( 10 , \text{L} + 20 , \text{L}