Question

В дневнике Поли в текущей четверти стоит 24 отметки по математике; в дневнике Тани — такое же число отметок по тому же предмету. Поля получила пятёрок столько же, сколько Таня четвёрок, четвёрок столько же, сколько Таня троек, троек столько же, сколько Таня двоек, и двоек столько же, сколько Таня – пятёрок. При этом средний балл в этой четверти у девочек одинаковый. Сколько двоек получила Поля?

Answer 1

Поля получила 0 двоек потому что Таня не получила не одной пятерки

Answer 2

Understanding the Problem

The problem states that in Polya's diary, there are 24 marks in mathematics, and in Tanya's diary, there are the same number of marks for the same subject. Polya received as many fives as Tanya received fours, as many fours as Tanya received threes, as many threes as Tanya received twos, and as many twos as Tanya received fives. The average score for the girls in this quarter is the same. We need to determine how many twos Polya received.

Solution

Let's assume that Polya received x twos. According to the problem, Tanya received the same number of twos as Polya received fives. Therefore, Tanya received x fives.

Since the average score for the girls is the same, we can calculate the average score using the formula:

Average Score = (Sum of Scores) / (Number of Scores)

In this case, the sum of scores for both girls is 24 + 24 = 48, and the number of scores is 24 + 24 = 48. Therefore, the average score is:

Average Score = 48 / 48 = 1

Now, let's calculate the sum of scores for Polya. Polya received x twos, so the sum of her scores is 2 * x. Additionally, Polya received the same number of fives as Tanya received fours, so the sum of her scores is also 5 * x. Therefore, we can write the equation:

2 * x + 5 * x = 48

Simplifying the equation, we get:

7 * x = 48

Solving for x, we find:

x = 48 / 7

Therefore, Polya received approximately 6.857 twos.

Answer

Polya received approximately 6.857 twos.

Verification

To verify the answer, we can substitute the value of x back into the equation and check if it satisfies the conditions of the problem.

Substituting x = 6.857 into the equation, we get:

2 * 6.857 + 5 * 6.857 = 48

13.714 + 34.285 = 48

48 = 48

The equation is satisfied, which means our answer is correct.