Based on the mixture described earlier, what is the price per gram of the mixture?

• A. $0.15 per gram
• B. $0.30 per gram
• C. $0.2375 per gram
• D. $0.50 per gram

Answer: (C)

When you mix items priced per gram, the overall price per gram is just the total cost divided by the total grams. It’s a weighted average of the two prices, with the weights being how much mass you take from each price.

If one part costs $0.15 per gram and another costs $0.30 per gram, the mixture’s price per gram must lie between those two numbers. The exact value is found from p_mix = (p1·m1 + p2·m2) / (m1 + m2). Setting p_mix to $0.2375 and solving, you get 0.2375(m1 + m2) = 0.15m1 + 0.30m2, which leads to m2 = 1.4 m1.

For a concrete example, take m1 = 40 g at $0.15/g and m2 = 56 g at $0.30/g. The total mass is 96 g and the total cost is 40(0.15) + 56(0.30) = 6 + 16.8 = 22.8. The price per gram is 22.8 / 96 = $0.2375 per gram, matching the given value.