Question

The average of 7 numbers is 60. The average of the first three numbers is 50, while the average of the last three is 70. What must be the remaining number?

Answer 1

From the last two facts, we get

`\frac{x_1+x_2+x_3}3=50\implies\frac{x_1+x_2+x_3}7=\frac{150}7`

`\frac{x_5+x_6+x_7}3=70\implies\frac{x_5+x_6+x_7}7=30`

Then

`\frac{x_1+x_2+\cdots+x_6+x_7}7=60\implies\frac{x_4}7=60-\frac{150}7-30\implies\boxed{x_4=60}`