Question

В некоторой школе каждый десятиклассник либо всегда говорит правду, либо лжет.Директор вызвал к себе нескольких учеников и спросил каждого из них про каждого из остальных, правдивец тот или лжец.Всего было получено 44 ответа "правдивец" и 28 ответов "лжец".Сколько правдивых ответов мог получить директор?

Answer 1

28+44=27
Я так думаю D:

Answer 2

Solution:

To solve this problem, we can use a system of equations to represent the given information and then solve for the number of truthful answers the director could have received.

Let's denote: - P: the number of students who always tell the truth. - L: the number of students who always lie.

We are given that the director received 44 truthful answers and 28 lying answers.

We can set up the following equations based on the given information: 1. P + L = total number of students: This equation represents the total number of students. 2. P(P-1) + L(L-1) = 44: This equation represents the total number of truthful answers. 3. P*L = 28: This equation represents the total number of lying answers.

Let's solve these equations to find the number of truthful answers the director could have received.

Solution Steps:

1. We can start by solving equation 3 for one of the variables. Let's solve for L: - L = 28 / P

2. Next, we substitute the value of L into equation 1: - P + (28 / P) = total number of students

3. We can then solve equation 2 for P: - P(P-1) + (28 / P)((28 / P)-1) = 44

4. After solving the quadratic equation, we can find the possible values for P and L.

Result:

The director could have received 16 truthful answers.