Question

В математической олимпиаде учавствовали 100 школьников было предложено четыре задачи . Первую задачу решили 90 человек вторую 80 третью 70 четвертую 60. При этом никто не решил все задачи . Награду получили те кто решил третью и четвертуую . Сколько человек было награждено?

Answer 1

всех решенных задач 60+70+80+90=300. Значит, в среднем один школьник решил 300:100=3 задачи. Т.к. 4 задачи не решил никто, значит, максимум, каждый школьник решил 3 задачи: или 1,2,3 или 1,2,4 или 1,3,4 или 2,3,4. Награду получили только те, кто решил 3 и 4 задачи, т.е. 1,3,4 и 2,3,4.  если получивших награду обозначить х, то (60-х) - кол-во учеников, решивших 1,2,3 задачи, а (70-х)-решивших 1,2,4 задачи. Получаем равенство
(60-Х) + (70-Х) + Х = 100
Х = 30
Было награждено 30 человек

Answer 2

Problem Analysis

In this mathematical olympiad, 100 schoolchildren participated and were given four problems to solve. The number of students who solved each problem is as follows: - Problem 1: 90 students - Problem 2: 80 students - Problem 3: 70 students - Problem 4: 60 students

It is mentioned that no one solved all four problems, and only those who solved the third and fourth problems received an award. We need to determine how many people were awarded.

Solution

To find the number of people who were awarded, we need to find the intersection of the students who solved the third problem and the students who solved the fourth problem.

Let's calculate the number of students who solved both the third and fourth problems:

- Number of students who solved the third problem: 70 - Number of students who solved the fourth problem: 60

To find the intersection, we take the smaller value, which is 60.

Therefore, 60 students were awarded for solving the third and fourth problems.

Conclusion

In the mathematical olympiad, 60 students were awarded for solving the third and fourth problems.