Question

Ученикам трех классов выдали 574 учебника. Каждый ученик получил одинаковое число книг. Известно, что в каждом классе больше 25, но меньше 30 учащихся. Сколько учебников получил каждый ученик и сколько всего учеников в трех классах?

Answer 1

Problem Analysis

We are given that 574 textbooks were distributed among the students of three classes. Each student received an equal number of textbooks. We also know that there are more than 25 but fewer than 30 students in each class. We need to determine how many textbooks each student received and the total number of students in the three classes.

Solution

Let's assume that each student received x textbooks. Since the number of textbooks distributed is 574, we can set up the following equation:

x * total_number_of_students = 574

To find the total number of students, we need to determine the factors of 574. We can do this by finding the prime factorization of 574.

The prime factorization of 574 is:

2 * 7 * 41

Since the number of students in each class is more than 25 but less than 30, we can eliminate the factors 2 and 7. Therefore, the only factor we can use is 41.

So, the total number of students in the three classes is 41.

To find the number of textbooks each student received, we can substitute the value of the total number of students into the equation:

x * 41 = 574

Solving for x, we get:

x = 574 / 41

Calculating this, we find that each student received approximately 14 textbooks.

Answer

Each student received approximately 14 textbooks, and there are a total of 41 students in the three classes.