An ore contains 7.8% aluminium. What mass of aluminium would there be in 50kg of the ore?

1. Break Down the Problem

To find the mass of aluminium contained in the ore, we need to calculate a percentage of the total mass of the ore. The specific percentage of aluminium in the ore is given as 7.8%, and the total mass of the ore is 50 kg.

2. Relevant Concepts

The formula to calculate the mass of aluminium can be expressed as: $\text{Mass of Aluminium} = \left( \frac{\text{Percentage of Aluminium}}{100} \right) \times \text{Total Mass of Ore}$

3. Analysis and Detail

1. The percentage of aluminium in the ore is 7.8%.
2. The total mass of the ore is 50 kg.
3. Substituting these values into the formula gives: $\text{Mass of Aluminium} = \left( \frac{7.8}{100} \right) \times 50$

4. Verify and Summarize

Now, perform the multiplication: $\text{Mass of Aluminium} = 0.078 \times 50 = 3.9 \text{ kg}$ Thus, the calculated mass of aluminium is 3.9 kg.

Final Answer

The mass of aluminium in 50 kg of the ore is 3.9 kg.