7. In a mathematics competition, 23 fourth-grade students participated. Some of them were supposed to have four classes that day, while others were supposed to have five. How many had four, and how many had five classes if all together they missed a total of 101 classes?

The use of a pocket calculator or any reference materials is not allowed.

## Ministry of Science and Education of the Republic of Croatia

Agency for Education and Upbringing

Croatian Mathematical Society

## SCHOOL/CITY COMPETITION IN MATHEMATICS
First solution.

| $\mathbf{4}$ hours of classes | $\mathbf{5}$ hours of classes | Total hours of classes |
| :---: | :---: | :---: |
| 5 students $\ldots . .20$ hours | $23-5=18$ students $\ldots 90$ hours | 110 hours |
| 6 students $\ldots .24$ hours | $23-6=17$ students $\ldots 85$ hours | 109 hours |
| 7 students $\ldots . .28$ hours | $23-7=16$ students $\ldots 80$ hours | 108 hours |
| 8 students $\ldots .32$ hours | $23-8=15$ students $\ldots 75$ hours | 107 hours |
| 9 students $\ldots .36$ hours | $23-9=14$ students $\ldots 70$ hours | 106 hours |
| 10 students $\ldots . .40$ hours | $23-10=13$ students $\ldots 65$ hours | 105 hours |
| $\ldots$ | $\ldots$ | $\ldots$ |

It is necessary to calculate at least 3 rows in the sequence to observe the rule of increasing and decreasing the total number of hours, which then needs to be explained.

Explanation: Each additional student in the class with 4 hours of classes reduces the total number of hours by one. $\quad 4$ POINTS (Alternatively: Each additional student in the class with 5 hours of classes increases the total number of hours by one.) $105-101=4$ hours less means 4 more students.

Note: If there is no explanation, then all possible options must be listed in the table for the maximum score (8 POINTS) in this part of the task. 2 POINTS are awarded for the written answer about the number of students in both classes.