Question

В олимпиаде по химии участвовало5 человек. на каждый вопрос один из них дал неправильный ответ, остальные - правильный. число правильных ответов у юры равно 10 - меньше , чем у других ,а у Тимофея равно 13 - больше чем у других . сколько всего вопросов было в олимпиаде?

Answer 1

Ответ ответ ответ ответ ответ ответ

Answer 2

Number of Questions in the Chemistry Olympiad

To determine the total number of questions in the chemistry Olympiad, we can use the information provided in the question.

Let's break down the given information:

- There were 5 participants in the Olympiad. - Each participant gave one incorrect answer, while the rest gave correct answers. - Yuri had 10 fewer correct answers than the others. - Timofey had 13 more correct answers than the others.

Based on this information, we can calculate the total number of questions in the Olympiad.

Let's assume the total number of questions is represented by x.

- Yuri had 10 fewer correct answers than the others, so he had (x - 10) correct answers. - Timofey had 13 more correct answers than the others, so he had (x + 13) correct answers. - The remaining 3 participants had the same number of correct answers, which we'll represent as y.

To find the total number of questions, we can set up the following equation:

(x - 10) + (x + 13) + 3y = 5x

Simplifying the equation:

2x + 13 + 3y = 5x

Rearranging the equation:

2x - 5x = -13 - 3y

-3x = -13 - 3y

Dividing both sides by -3:

x = (13 + 3y) / 3

Since the number of questions must be a positive integer, we need to find a value of y that makes x an integer.

Let's try different values of y and calculate the corresponding value of x:

- For y = 1, x = (13 + 3) / 3 = 16 / 3, which is not an integer. - For y = 2, x = (13 + 6) / 3 = 19 / 3, which is not an integer. - For y = 3, x = (13 + 9) / 3 = 22 / 3, which is not an integer. - For y = 4, x = (13 + 12) / 3 = 25 / 3, which is not an integer. - For y = 5, x = (13 + 15) / 3 = 28 / 3, which is not an integer. - For y = 6, x = (13 + 18) / 3 = 31 / 3, which is not an integer. - For y = 7, x = (13 + 21) / 3 = 34 / 3, which is not an integer. - For y = 8, x = (13 + 24) / 3 = 37 / 3, which is not an integer. - For y = 9, x = (13 + 27) / 3 = 40 / 3, which is not an integer. - For y = 10, x = (13 + 30) / 3 = 43 / 3, which is not an integer.

Based on these calculations, we can see that there is no integer value of y that makes x an integer. Therefore, we cannot determine the total number of questions in the chemistry Olympiad with the given information.

Please let me know if there is anything else I can help you with!