Question

В классной комнате стоят парты. Если за каждую парту посадить по 1 ученику, то семи ученикам не хватит места, а если посадить по 2 ученика, то 5 парт останутся свободными. Определите число парт и число учеников в классе.

Answer 1

Problem Analysis

We are given a scenario where there are desks in a classroom. If we seat one student per desk, there won't be enough space for seven students. However, if we seat two students per desk, there will be five desks left empty. We need to determine the number of desks and the number of students in the class.

Solution

Let's assume the number of desks in the classroom is x and the number of students is y.

According to the problem statement, if we seat one student per desk, there won't be enough space for seven students. This can be represented by the equation:

x - 7 < y Similarly, if we seat two students per desk, there will be five desks left empty. This can be represented by the equation:

x - 5 = 2y We can solve this system of equations to find the values of x and y.

Solving the System of Equations

Let's solve the system of equations using substitution or elimination method.

From equation we can rewrite it as:

x = 2y + 5 Substituting equation into equation we get:

2y + 5 - 7 < y

Simplifying the inequality:

y < 2

Since y represents the number of students, it must be a positive integer. Therefore, the only possible value for y is 1.

Substituting y = 1 into equation we can solve for x:

x = 2(1) + 5

Simplifying:

x = 7

Therefore, the number of desks in the classroom is 7 and the number of students is 1.

Answer

The number of desks in the classroom is 7 and the number of students is 1.