## Task 4 - 180514

On a parking lot, there are a total of 60 passenger cars of the types "Trabant", "Wartburg", "Skoda", and "Wolga". The number of cars of the type "Trabant" is twice as large as the number of cars of the other three types combined. Additionally:

There are three times as many cars of the type "Wartburg" as of the types "Skoda" and "Wolga" combined, and three more cars of the type "Skoda" than of the type "Wolga".

How many cars of each type are on this parking lot?
If the "Trabant" cars are divided into two groups of equal number, then all the remaining cars form a third group of the same number. Each group therefore contains 20 cars, so there are 40 "Trabant" cars in the parking lot. For the remaining 20 cars:

If the "Wartburg" cars are divided into three groups of equal number, then the remaining cars now form a fourth group of the same number. Thus, each of these groups contains 5 cars, so there are 15 "Wartburg" cars in the parking lot. For the remaining 5 cars:

They are only of the types "Wolga" and "Skoda." According to the problem, the number of "Skoda" cars is three more than the number of "Wolga" cars. This is only possible if there are 4 "Skoda" cars and 1 "Wolga" car in the parking lot.

Solutions of the I. Round 1978 adopted from [5]

### 2.19.2 II. Round 1978, Class 5