Problem 1. The arithmetic mean of four numbers is 20. After adding one more number, the arithmetic mean of the five numbers will be 18. What is the added number?
Solution. Since the arithmetic mean of the four numbers is 20, the sum of the four numbers is 80, that is

$$
x_{1}+x_{2}+x_{3}+x_{4}=80
$$

The arithmetic mean of the five numbers is 18, that is

$$
x_{1}+x_{2}+x_{3}+x_{4}+x_{5}=5 \cdot 18, \text { i.e. } 80+x_{5}=90
$$

From this, $x_{5}=10$.