Question

The mean weight of a class of 34 students is 46.5 kg. If the weight of the teacher is included, the mean is rises by 500 g. Find the weight of the teacher.

Answer 1

Mean weight of 34 students = 46.5 kg
Sum of the weights of 34 students = $(46.5\times 34)\mathrm{kg}=1581$ kg
Increase in the mean weight when the weight of the teacher is included = 500 g = 0.5 kg
∴ New mean weight = (46.5 + 0.5) kg = 47 kg
Now,
Let the weight of the teacher be x kg.
Thus, we have:

$$\begin{gathered} \frac{\mathrm{Sum}\mathrm{of}\mathrm{the}\mathrm{weights}\mathrm{of}34\mathrm{students}+\mathrm{Weight}\mathrm{of}\mathrm{the}\mathrm{teacher}}{35}=47 \\ \Rightarrow \frac{1581+x}{35}=47 \\ \Rightarrow 1581+x=1645 \\ \Rightarrow x=64 \end{gathered}$$

Therefore, the weight of the teacher is 64 kg.