# Task 4.

In two departments of the "Phantasmagoria" laboratory, mobile applications for Android and iOS are being developed. On one of the working days, all employees of these departments exchanged a certain number of messages. Each developer from the Android department sent 7 and received 15 messages, while each developer from the iOS department sent 15 and received 9 messages. Messages could be sent to either a colleague in their own department or in the other department. In which department are there more employees?
# Solution.

Let $n$ be the number of people working in the Android department, and $m$ be the number of people working in the iOS department. We will calculate the total number of messages in two ways.

The number of messages sent is $7 n + 15 m$.

The number of messages received is $15 n + 9 m$.

Then,

$$
7 n + 15 m = 15 n + 9 m
$$

Olympiad for School Students "Hope of Energy". Final Stage. Solutions

from which

$$
6 m = 8 n
$$

Since the first multiplier on the left is smaller, the second must be larger. Therefore, $m > n$.

Answer: There are more people in the iOS department.