What is the cost per kilogram of a 50:50 blend of substances costing $3/kg and $5/kg?

To determine the cost per kilogram of a 50:50 blend of two substances costing $3 per kilogram and $5 per kilogram, you can start by calculating the total cost of the blend.

In this case, since the blend is 50:50, you would take one kilogram of the first substance and one kilogram of the second substance.

1. The cost of the first substance is $3 for 1 kilogram.

2. The cost of the second substance is $5 for 1 kilogram.

Now, you add the costs together:

[

\text{Total Cost} = \text{Cost of first substance} + \text{Cost of second substance} = 3 + 5 = 8

]

Since you have 2 kilograms in total (1 kilogram of each substance), you then calculate the cost per kilogram of the blend by dividing the total cost by the total weight:

[

\text{Cost per kilogram} = \frac{\text{Total Cost}}{\text{Total Weight}} = \frac{8}{2} = 4

]

This result shows that the cost per kilogram of the 50:50 blend is $4. The method of averaging the costs based on their proportions