## Task 4 - 320524

In a house with a ground floor and three additional floors, 72 people live. On the second floor, there are 7 more people than on the first floor, and on the third floor, there are 6 more people than on the first floor.

Since there is also a store in addition to apartments on the ground floor, there are 12 fewer people living there than on the first floor.

How many people live on the ground floor and on each of the other floors?

Explain how these numbers of people can be derived from the above information and verify that the numbers you provide meet these conditions!
From the given information:

On the first floor, 12 more people live than on the ground floor.

On the second floor, $12+7=19$ more people live than on the ground floor.

On the third floor, $12+5=17$ more people live than on the ground floor.

If these mentioned $12+19+17=48$ people were to move out, then in each floor, the same number of people would remain as on the ground floor; that is, in the entire house, the fourfold number of residents of the ground floor would remain. Since 72 - $48=24$ people remained in the house, it follows: On the ground floor, $24: 4=6$ people live.

From this and the comparative statements mentioned at the beginning, it follows:

On the first floor, $6+12=18$ people live, on the second floor, $6+19=25$ people live, on the third floor, $6+17=23$ people live.

Solutions of the II. Round 1992 taken from [5]

### 2.34 XXXIII. Olympiad 1993

### 2.34.1 I. Round 1993, Class 5