7. At the entrance to the cinema hall, among 30 visitors, 58 candies were distributed. Each girl received six candies, each boy received four candies, and each adult received one candy. How many girls, how many boys, and how many adults could there be in the cinema hall?

## Ministry of Science and Education of the Republic of Croatia  Agency for Education and Upbringing  Croatian Mathematical Society

## SCHOOL COMPETITION IN MATHEMATICS  January 26, 2024.
First solution.

After each visitor eats 1 candy, there are $58-30=28$ candies left in the hall.

Then the adults do not have any candies.
\[\begin{array}{ll}\text { Each boy has } 3 \text { candies left, so the number of candies with boys is a multiple of 3. } & 1 \text { POINT } \\ \text { Each girl has } 5 \text { candies left, so the number of candies with girls is a multiple of 5. } & 1 \text { POINT } \\ \text { The number of candies with girls is not greater than } 28 \text {, so the possible number of candies with girls is } \\ 5,10,15,20 \text { and } 25 . & \\ \text { 1 POINT }\end{array}\]

Then the boys would have $23,18,13,8$ and 3 candies left, but only 18 and 3 are multiples of 3.

2 POINTS

If the boys have a total of 18 candies, then the girls have 10 candies.

Then there are $18: 3=6$ boys and $10: 5=2$ girls in the hall.

1 POINT

There are $30-(6+2)=22$ adults in the hall.

1 POINT

If the boys have 3 candies, then the girls have 25 candies, so there is $3: 3=1$ boy and $25: 5=5$ girls in the hall.

1 POINT

There are $30-(1+5)=30-6=24$ adults in the hall.

1 POINT

There could be 1 boy, 5 girls, and 24 adults in the hall, or

6 boys, 2 girls, and 22 adults in the hall.

TOTAL 10 POINTS