In a two-story house, which is inhabited not only on both floors but also in the basement, 35 people live above someone and 45 people live below someone. At the same time, one third of all the people living in the house live on the 1st floor.

How many people live in the house in total?

(L. Hozová)
People who live above someone are residents of the 2nd and 1st floors. People who live below someone are residents of the 1st floor and the ground floor. In the sum $35+45=80$, the residents of the 1st floor are counted twice.

If we denote the number of residents on the 1st floor by $p$, then the total number of residents in the building can be expressed as either $80-p$ or $3p$. From this, we get the equation, which we can easily solve:

$$
\begin{aligned}
3 p & =80-p, \\
4 p & =80, \\
p & =20 .
\end{aligned}
$$

There are a total of 60 people living in the building.

Evaluation. 2 points for the observation that the residents of the 1st floor are counted twice in the sum $35+45$; 2 points for setting up and solving the equation; 2 points for the total number of people in the building.

Note. If $d, p$, and $z$ represent the number of residents on the 2nd floor, the 1st floor, and the ground floor, respectively, then from the problem statement we have

$$
d+p=35, \quad p+z=45, \quad d+p+z=3 p .
$$

From this, we can express all unknowns in various ways: $d=15, p=20$, and $z=25$. Such solutions should be evaluated with 2 points for setting up the equations, 2 points for solving them, and 2 points for the conclusion.