Question

На математической олимпиаде участникам было предложено 10 задач. За каждую правильно решенную задачу засчитывали 5 баллов, а за каждую нерешенную или решенную неверно – отнимали 3 балла. Один участник получил 34 балла. Сколько задач он решил правильно? Решите пожалуйста.

Answer 1

Пусть участник решил правильно x задач. Значит, он не решил 10-x задач. Таким образом, ему засчитали 5x баллов и отняли 3(10-x)=30-3x баллов. Значит, 5x-(30-3x)=34, откуда 5x-30+3x=34, 8x=64, x=8, то есть, участик решил 8 задач. Действительно, в этом случае ему начислили 8*5=40 баллов и сняли 2*3=6 баллов, в итоге он получил 34 балла.

Ответ: 8 задач.

Answer 2

Problem Analysis

In this problem, participants were given 10 math problems to solve. Each correctly solved problem is worth 5 points, while each unsolved or incorrectly solved problem results in a deduction of 3 points. We need to determine how many problems the participant solved correctly based on their total score of 34 points.

Solution

Let's assume that the participant solved x problems correctly. Since each correctly solved problem is worth 5 points, the total score from the correctly solved problems would be 5x.

The participant also received a deduction of 3 points for each unsolved or incorrectly solved problem. Since the total score is 34 points, we can calculate the deduction as follows: 10 - x (since there are 10 problems in total and the participant solved x problems correctly).

Therefore, the equation for the total score can be written as: 5x - 3(10 - x) = 34.

Simplifying the equation, we have: 5x - 30 + 3x = 34.

Combining like terms, we get: 8x - 30 = 34.

Adding 30 to both sides of the equation, we have: 8x = 64.

Dividing both sides of the equation by 8, we get: x = 8.

Therefore, the participant solved 8 problems correctly.

Answer

The participant solved 8 problems correctly.