Question

The table below shows the carbon content of four samples of powdered coal. If these four samples are mixed completely, what would be the resultant carbon percentage of the mixture by weight? 

• A. 58 %
• B. 86 %
• C. 87 %
• D. 90 %

Hint:

When mixing different samples with varying concentrations, the resultant concentration can be found using the weighted average formula, considering the mass of each sample.

Answer 1

The Correct Option is B

To find the resultant carbon percentage by weight of the mixture, we can use the weighted average formula:

\[ \text{Weighted average} = \frac{\sum \left( \text{mass of sample} \times \text{carbon percentage} \right)}{\sum \left( \text{mass of sample} \right)}. \]

Step 1: Calculate the total mass of the mixture.
The total mass is the sum of the masses of all the samples:

\[ \text{Total mass} = 2 + 1 + 2 + 1 = 6 \, \text{kg}. \]

Step 2: Calculate the weighted sum of the carbon percentages.

\[ \text{Weighted sum} = (2 \times 88) + (1 \times 90) + (2 \times 80) + (1 \times 90) = 176 + 90 + 160 + 90 = 516. \]

Step 3: Calculate the weighted average carbon percentage.

\[ \text{Carbon \%} = \frac{516}{6} = 86 \%. \]

Final Answer:

\[ \boxed{86 \%}. \]