The average of 11 results in 50

Question

The average of 11 results in 50.If the average of first six results is 48 and that of last six 51,the sixth result is?

Answer 1

We have the following system of equations:

$$x_1+\cdots+x_{11}=50\cdot11 \tag{1}$$ $$x_1+\cdots+x_{6}=48\cdot6 \tag{2}$$ $$x_6+\cdots+x_{11}=51\cdot6 \tag{3}$$

Adding (2) and (3), we obtain: $$x_1+\cdots+2x_6+\cdots +x_{11}=6\cdot(48+51)=6\cdot99.$$

Substituting in (1), $$x_6+50\cdot11=6\cdot99 \implies x_6=44.$$