Question

В некоторой школе более 90% учеников знают английский и немецкий языки, и более 90% учеников знают английский и французский языки. Докажите, что среди учеников, знающих немецкий и французский языки, более 90% знают английский язык. ответьте пожалуйста на вопрос!

Answer 1

Ответ:Пусть a школьников знают все три языка, b – только английский и немецкий, c – только английский и французский, d – только немецкий и французский. По условию  a + b > 9(c + d),  a + c > 9(b + d).  Взяв полусумму, получим  a > 9d + 4(b + c),  тем более  a > 9d,  а это и требовалось.

Объяснение:

Answer 2

Given Information

In a certain school, more than 90% of the students know English and German languages, and more than 90% of the students know English and French languages.

To Prove

We need to prove that among the students who know German and French languages, more than 90% of them know English.

Proof

Let's assume that there are 100 students in the school.

According to the given information: - More than 90% of the students know English and German languages. - More than 90% of the students know English and French languages.

Let's represent the number of students who know English and German languages as EG, the number of students who know English and French languages as EF, and the number of students who know English, German, and French languages as EGF.

We can write the following equations based on the given information: - EG > 0.9 * 100 - EF > 0.9 * 100

Now, let's consider the students who know German and French languages. We can represent this as GF.

Since all the students who know German and French languages also know English, we can write the following equation: - GF = EGF

To prove that more than 90% of the students who know German and French languages also know English, we need to show that EGF > 0.9 * GF.

From the given information, we know that: - EG > 0.9 * 100 - EF > 0.9 * 100

Since all the students who know English, German, and French languages also know English, we can write the following equation: - EGF = EG

Therefore, we can conclude that EGF > 0.9 * GF, which means that more than 90% of the students who know German and French languages also know English.

Note: The actual numbers and percentages may vary based on the specific data provided. The above proof is a general explanation of how to approach the problem.