Question

5. Средний возраст одиннадцати игроков футбольной команды – 23 года. Когда одного игрока, получившего травму, заменили во время игры, средний возраст игроков на футбольном поле составил 22 года. На сколько лет ушедший с поля игрок моложе или старше нового игрока, вступившего в игру? 1) старше на 10 лет 2) моложе на 10 лет 3) старше на 11 лет 4) моложе на 11 лет 5) они ровесники 6) правильного ответа нет

Answer 1

Правильный ответ: Моложе на 11 лет.

Answer 2

Problem Analysis

We are given that the average age of eleven football players is 23 years. When one injured player is replaced during the game, the average age of the players on the field becomes 22 years. We need to determine whether the player who left the field is younger or older than the new player who entered the game.

Solution

Let's assume the age of the player who left the field is x years, and the age of the new player who entered the game is y years.

We can use the concept of averages to solve this problem. The average age of the eleven players before the substitution is 23 years, so the sum of their ages is 11 * 23 = 253 years.

After the substitution, the average age becomes 22 years, so the sum of the ages of the players on the field is 11 * 22 = 242 years.

We know that the sum of the ages of the players on the field after the substitution is equal to the sum of the ages of the players before the substitution minus the age of the player who left the field plus the age of the new player who entered the game.

Mathematically, we can represent this as:

253 - x + y = 242

Simplifying the equation, we get:

y - x = 242 - 253

y - x = -11

This equation tells us that the difference between the ages of the new player and the player who left the field is -11 years.

To determine whether the player who left the field is younger or older than the new player, we need to compare the values of x and y.

If y - x = -11, it means that the new player is 11 years younger than the player who left the field. Therefore, the correct answer is option 4) molozhe na 11 let.

Conclusion

The player who left the field is 11 years older than the new player who entered the game.