Question

Участнику олимпиады сразу насчитывается 100 баллы. За каждую правильно розвязану задачу количество баллов увеличивается на 10% за каждую неправильно розвязану задачу уменьшаются на 10% После розвязування нескольких задач участник приобрел 80,19 баллов. Сколько задач он розвязав правильно?

Answer 1

Пусть х - количество правильных ответов,
тогда (20 - х) - количество неправильных ответов.
Количество баллов, полученных за правильные ответы:
12х.
Количство баллов, снятых за неправильные ответы:
10(20 - х) = 200 - 10х.

12х - (200 - 10х) = 86
12х - 200 + 10х = 86
22х = 86 + 200
22х = 286
х = 286 : 22
х = 13 - количество правильных ответов.
Ответ: 13.

Answer 2

Calculation of Points for Each Problem

According to the given information, each problem solved correctly earns the participant an additional 10% of the current total score, while each problem solved incorrectly deducts 10% of the current total score. The participant starts with 100 points.

Calculation of the Final Score

The participant acquired a total of 80.19 points after solving several problems.

To determine the number of problems the participant solved correctly, we can work backward from the final score of 80.19 points.

Let's assume the participant solved "x" problems correctly.

Calculation Steps

1. Start with the initial score of 100 points. 2. For each problem solved correctly, add 10% of the current score. 3. For each problem solved incorrectly, deduct 10% of the current score.

Using these steps, we can calculate the final score based on the number of problems solved correctly.

Mathematical Calculation

Let's calculate the final score based on the number of problems solved correctly:

1. Start with the initial score of 100 points. 2. For each problem solved correctly, add 10% of the current score. 3. For each problem solved incorrectly, deduct 10% of the current score.

Based on the given information, the participant acquired a total of 80.19 points. Let's calculate the number of problems solved correctly:

1. Start with the initial score of 100 points. 2. For each problem solved correctly, add 10% of the current score. 3. For each problem solved incorrectly, deduct 10% of the current score.

Let's assume the participant solved "x" problems correctly.

The calculation can be represented as follows:

100 + x * (10% of 100) - (total number of problems - x) * (10% of 100) = 80.19

Simplifying the equation:

100 + 0.1x - 0.1(total number of problems - x) = 80.19

100 + 0.1x - 0.1(total number of problems) + 0.1x = 80.19

0.2x - 0.1(total number of problems) = 80.19 - 100

0.2x - 0.1(total number of problems) = -19.81

0.2x - 0.1x = -19.81 + 0.1(total number of problems)

0.1x = -19.81 + 0.1(total number of problems)

0.1x = -19.81 + 0.1(total number of problems)

0.1x = 0.1(total number of problems) - 19.81

x = (0.1(total number of problems) - 19.81) / 0.1

x = (total number of problems - 198.1) / 1

x = total number of problems - 198.1

Therefore, the participant solved (total number of problems - 198.1) correctly.

Please note that the exact number of problems solved correctly cannot be determined without knowing the total number of problems attempted by the participant.