Question

Учитель задал на лето задание Отличникову и Двоечникову, причем Двоечникову в четыре раза больше задач, чем Отличникову. После каникул оказалось, что они решили поровну задач, и процент задач, решенных Двоечниковым, равен проценту задач, не решенных Отличниковым. Какой процент задач решил Отличников?

Answer 1

Х - кол-во задач отличника, 4х - кол-во задач двоечника. у - процент решенных задач отличником, (100-у) - процент не решенных задач двоечником. т.к задач решено поровну, то составляем равенство
х*у=4х*(100-у), решаем икс сокращаем
у=4(100-у)
у=400-4у
5у=400
5у=400
у=80
вот так

Answer 2

Problem Analysis

To solve this problem, we need to determine the percentage of tasks solved by the "Отличник" (top-performing student). We are given that the "Двоечник" (lower-performing student) was assigned four times as many tasks as the "Отличник." After the vacation, it is revealed that they solved an equal number of tasks, and the percentage of tasks solved by the "Двоечник" is equal to the percentage of tasks unsolved by the "Отличник."

Solution

Let's assume that the number of tasks assigned to the "Отличник" is x. According to the problem, the "Двоечник" was assigned four times as many tasks, so the number of tasks assigned to the "Двоечник" is 4x.

After the vacation, we are told that they solved an equal number of tasks. Let's denote the number of tasks solved by both students as y.

We are also given that the percentage of tasks solved by the "Двоечник" is equal to the percentage of tasks unsolved by the "Отличник." This means that the percentage of tasks solved by the "Отличник" is equal to 100% minus the percentage of tasks solved by the "Двоечник."

To find the percentage of tasks solved by the "Отличник," we need to calculate the ratio of tasks solved by the "Отличник" to the total number of tasks assigned to the "Отличник" and then multiply by 100.

Calculation

Let's calculate the percentage of tasks solved by the "Отличник" step by step:

1. The number of tasks assigned to the "Отличник" is x. 2. The number of tasks assigned to the "Двоечник" is 4x. 3. The total number of tasks solved by both students is y. 4. The percentage of tasks solved by the "Двоечник" is 100 - (y / 4x) * 100. 5. The percentage of tasks solved by the "Отличник" is (y / x) * 100.

Calculation Example

Let's assume that the number of tasks solved by both students (y) is 20. We can substitute this value into the calculations:

1. The number of tasks assigned to the "Отличник" is x. 2. The number of tasks assigned to the "Двоечник" is 4x. 3. The total number of tasks solved by both students is y = 20. 4. The percentage of tasks solved by the "Двоечник" is 100 - (20 / 4x) * 100. 5. The percentage of tasks solved by the "Отличник" is (20 / x) * 100.

Conclusion

To determine the exact percentage of tasks solved by the "Отличник," we need to know the value of x and y. Without this information, we cannot provide a specific answer. However, we have provided the general formula and steps to calculate the percentage based on the given conditions.

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