## SUBJECT 4

On Friendship Day, each student in the 5th grade A class gives a greeting card to each classmate. This year, students from another class also joined in, exchanging 2726 more greeting cards than last year. Knowing that there are at least 25 students in each class, find out how many greeting cards were exchanged last year.

## Note:

Working time: 2 hours.

All subjects are mandatory.

Each subject is graded from 0 to 7.

No points are awarded by default.
## SUBJECT 4

Let $x$ be the number of students in class $\mathrm{a} \mathrm{V}$-a $\mathrm{A}$ and $y$ be the number of students in the other class. $x \cdot y + y \cdot x + y \cdot(y-1)$ additional congratulations ....................................................1p

![](https://cdn.mathpix.com/cropped/2024_06_07_3480621dd5c5c8cebb70g-2.jpg?height=54&width=1262&top_left_y=2126&top_left_x=197)

![](https://cdn.mathpix.com/cropped/2024_06_07_3480621dd5c5c8cebb70g-2.jpg?height=51&width=1277&top_left_y=2173&top_left_x=184)

![](https://cdn.mathpix.com/cropped/2024_06_07_3480621dd5c5c8cebb70g-2.jpg?height=51&width=1277&top_left_y=2219&top_left_x=184)
$y \geq 25$ and $x \geq 25 \Rightarrow 2 x + y - 1 \geq 74 \Rightarrow$ unique solution ..................................1p $x \cdot(x-1) = 33 \cdot 32 = 1056$ the number of congratulations exchanged last year ........1p