In the parking lot, there were cars and bicycles. If one more car arrived, there would be as many of them as there are bicycles. If five more bicycles arrived, all the bicycles would have as many wheels as all the cars.

How many cars and how many bicycles were in the parking lot?

(M. Dillingerová)

Hint. Imagine a situation where the number of wheels of the cars and bicycles is the same.
A car has four wheels, a bicycle has two; one car has the same number of wheels as two bicycles.

There was one more bicycle than cars in the parking lot. Consider the situation where there would be five more bicycles in the parking lot than originally, that is, the situation where the number of wheels would match. In such a case, there would be six more bicycles than cars.

Six more bicycles mean 12 more wheels. This difference corresponds to exactly six cars (a car has two more wheels than a bicycle and $2 \cdot 6=12$). Therefore, there were six cars and seven bicycles (one more than cars) in the parking lot.

Notes. The reasoning in the last paragraph can be replaced by testing possibilities, where the numbers of vehicles are gradually increased and their difference is checked:

| cars | 3 | 4 | 5 | 6 | $\ldots$ |
| :---: | :---: | :---: | :---: | :---: | :---: |
| bicycles | 6 | 8 | 10 | 12 | $\ldots$ |
| difference | 3 | 4 | 5 | $\mathbf{6}$ | $\ldots$ |

The observed difference keeps increasing, so the problem has no other solution.

If we assume that each car also has one spare wheel, then by similar reasoning we would conclude that there were four cars and five bicycles in the parking lot.