Question

В зале стояли одинаковые скамейки.Если на каждую скамейку посадить двоих учеников,то то семи ученикам не хватит места. Если же на каждую скамейку сядут 3 ученика, то 5 скамеек останутся свободными.Сколько в зале скамеек и сколько учеников нужно разместить.Решить задачу

Answer 1

х (шт.) - количество скамеек

1 случай: х*2+7 = 2х+7- на каждой скамейке по 2 уч. + 7 лишних учеников, 

2 случай: х*3-15 = 3х-15 - на каждой скамейке по 3 уч., а чтобы занять 5 свободных, не хватает 3*5=15 учеников

Составим ур-е:

2х+7=3х-15

х=22 (скамейки) в зале

2*22+7=51 (уч) - нужно зазместить

Проверка:

1 случай:51-(22*2)=7

51-44=7 (уч) не хватило места

7=7

2 случай: 51:3=17 (скамеек) - надо, если по 3 уч. на 1 скамейку

22-17=5(скамеек) - останутся свободными

5=5

Ответ: в зале 22 скамейки и 51 ученик

Answer 2

Problem Analysis

We are given that there are the same number of benches in a room. If two students are seated on each bench, there will not be enough space for seven students. However, if three students are seated on each bench, five benches will remain empty. We need to determine the number of benches in the room and the number of students that need to be accommodated.

Solution

Let's assume there are x benches in the room and y students that need to be accommodated.

According to the problem statement, if two students are seated on each bench, there will not be enough space for seven students. This can be represented by the equation:

2x < y + 7

Similarly, if three students are seated on each bench, five benches will remain empty. This can be represented by the equation:

3x + 5 = y

We can solve these two equations simultaneously to find the values of x and y.

Solving the Equations

Let's solve the equations:

2x < y + 7 --> Equation 1 3x + 5 = y --> Equation 2

To solve these equations, we can use substitution or elimination method. Let's use the substitution method.

From Equation 2, we can express y in terms of x:

y = 3x + 5

Substituting this value of y in Equation 1:

2x < 3x + 5 + 7 2x < 3x + 12 2x - 3x < 12 -x < 12 x > -12

Since the number of benches cannot be negative, we can ignore the negative solution. Therefore, x > 0.

Now, let's substitute the value of x in Equation 2 to find y:

3x + 5 = y 3(x) + 5 = y 3x + 5 = y

So, the number of benches in the room is x and the number of students that need to be accommodated is y.

Answer

Based on the given information, we have determined that the number of benches in the room is x and the number of students that need to be accommodated is y. However, we cannot determine the exact values of x and y without additional information or constraints.