Question

Если участников собрания рассадить по 6 человек за каждый стол ,то троим не хватит мест . А если этих же участников рассадить по 9 человек за каждый стол, то 2 стала останутся не занятыми.сколько человек участвовало на собрании .

Answer 1

45 человек.......................

Answer 2

Calculating the Number of Participants at the Meeting

To solve this problem, we can use a simple algebraic approach. Let's denote the total number of participants as P and the total number of tables as T.

According to the given information: 1. When participants are seated 6 per table, three people are left without a seat. 2. When participants are seated 9 per table, two tables are left unoccupied.

We can express this information in the form of equations:

Equation 1: P mod 6 = 3 (When seated 6 per table, three people are left without a seat) Equation 2: P mod 9 = 0 (When seated 9 per table, no tables are left unoccupied)

Let's solve these equations to find the value of P.

Solving the Equations

First, let's solve Equation 1: P mod 6 = 3

The solutions to this equation are: P = 6n + 3, where n is a non-negative integer (0, 1, 2, ...)

Next, let's solve Equation 2: P mod 9 = 0

The solutions to this equation are: P = 9m, where m is a non-negative integer (0, 1, 2, ...)

Finding the Common Solution

We need to find a common solution for both equations. This means finding a value of P that satisfies both Equation 1 and Equation 2.

The common solution to both equations is the least common multiple (LCM) of 6 and 9, which is 18.

So, the total number of participants at the meeting is 18.

Therefore, the number of people who participated in the meeting is 18.