[ Divisibility of numbers. General properties ]

On a bus rode Andrey

To the circle and back home,

Paying 115 rubles,

He bought himself a pass.

In January he didn't get it,

And therefore for several days

He bought a ticket from the driver

For 15 rubles for himself.

And on another day the conductor

Took only 11 rubles from him.

Returning from his circle

Every time he walked home our Andrey.

For January, how much money was spent,

The thrifty Andrey calculated:

To his surprise, he got

Exactly 115 rubles!

Calculate now as quickly as you can,

How many times the circle was in January

#
The amount of rubles spent by Andrey on the days when he bought a ticket from the driver is divisible by 5; the total amount of rubles spent by him in January is also divisible by 5. Therefore, the total amount of money spent on other days is also divisible by 5. Hence, the number of days when Andrey bought a ticket from the conductor is divisible by 5. The numbers 0 and 10 are not suitable; numbers greater than 10 are even less suitable, so the only possible option is 5 days. Then the number of other days is $(115-11 \cdot 5): 15=4$, and the circle was 9 times.

## Answer

9 times.