Question

В зале стоят одинаковые скамейки если на каждую скамейку посадить двоих учеников то 7 ученикам не хватит мест если на каждую скамейку сядут три ученика топ 5 скамеек останутся свободными Сколько в зале скамеек и Сколько учеников нужно на них рассадить Реши задачу алгебраическим способом

Answer 1

( х ) учеников, ( у ) скамеек. тогда ( составляем два уравнения)
1. Уравнение для числа учеников. По два  ученика на каждой скамейке и ещё семеро стоят, вместе получается общее число учеников.2*х+7=у.
2. Уравнение для числа скамеек. Все ученики расселись по трое на скамейку, и ещё пять скамеек осталось. у/3+5=х
3. Решаем систему уравнений. Вместо "у" во втором уравнении записываем выражение  из первого уравнения и приводим к общему знаменателю. Получаем: 2х+7+15=3х. Решаем: х=22-это число скамеек.
4. Подставляем найденный результат в первое уравнение и получаем   у=2*22+7=51 -это число учеников.
Ответ: 22 скамеек, 51 ученик.

Answer 2

Problem Analysis

We are given the following information: - If two students are seated on each bench, there will not be enough seats for 7 students. - If three students are seated on each bench, 5 benches will remain empty.

We need to determine the number of benches in the hall and the number of students that need to be seated on them.

Solution

Let's assume there are x benches in the hall.

If two students are seated on each bench, the total number of students that can be seated is 2x.

According to the problem, if 2x is less than 7, there will not be enough seats for 7 students. So we can write the inequality:

2x < 7

Solving this inequality, we find:

x < 7/2

Since the number of benches cannot be a fraction, we take the ceiling value of 7/2, which is 4.

So, if two students are seated on each bench, there are 4 benches in the hall.

Now, let's consider the case where three students are seated on each bench.

If three students are seated on each bench, the total number of students that can be seated is 3x.

According to the problem, if 3x is greater than 5, 5 benches will remain empty. So we can write the inequality:

3x > 5

Solving this inequality, we find:

x > 5/3

Since the number of benches cannot be a fraction, we take the floor value of 5/3, which is 1.

So, if three students are seated on each bench, there is 1 bench in the hall.

Therefore, the number of benches in the hall is 4 and the number of students needed to be seated on them is 2 * 4 = 8.

Answer

There are 4 benches in the hall and 8 students need to be seated on them.

Please let me know if I can help you with anything else.