Question

В конкурсе «Волшебный сундучок» приняло участие 25 восьмиклассников школы. Из них 80% правильно решили не менее одной задачи. Среди школьников, решивших более одной задачи, ровно четвёртая часть решила правильно, по крайней мере, 3 задачи; а 4 задачи решила правильно ровно треть учащихся, решивших не менее трёх задач. Сколько учащихся правильно решили ровно одну задачу?

Answer 1

80% * 25 = 20 - решили одну и более задачи
20 * 1/4 = 5 - решили 3 задачи
15 * 1/3 = 5 - решили 4 задачи
20 - 5 - 5 = 10 чел - решили одну задачу

думаю, что так

если помогла - поставь лучший ответ

Answer 2

Task Analysis

We are given the following information: - 25 eighth-grade students participated in the "Magical Chest" competition. - 80% of them correctly solved at least one problem. - Among the students who solved more than one problem, one-fourth of them correctly solved at least 3 problems. - One-third of the students who solved at least 3 problems correctly solved exactly 4 problems.

We need to determine the number of students who correctly solved exactly one problem.

Solution

Let's break down the information given and solve the problem step by step.

1. 80% of the students correctly solved at least one problem. - This means that 80% of 25 students, which is 20 students, solved at least one problem. 2. Among the students who solved more than one problem, one-fourth of them correctly solved at least 3 problems. - This means that 1/4 of the students who solved more than one problem correctly solved at least 3 problems. - Let's assume the number of students who solved more than one problem is "x". - Therefore, (1/4) * x students correctly solved at least 3 problems.

3. One-third of the students who solved at least 3 problems correctly solved exactly 4 problems. - This means that 1/3 of the students who solved at least 3 problems correctly solved exactly 4 problems. - Let's assume the number of students who solved at least 3 problems is "y". - Therefore, (1/3) * y students correctly solved exactly 4 problems.

To find the number of students who correctly solved exactly one problem, we need to subtract the students who solved more than one problem and those who solved at least 3 problems from the total number of students who solved at least one problem.

Let's calculate the values of "x" and "y" and then find the number of students who correctly solved exactly one problem.

Calculation

1. 80% of 25 students = 20 students2. Let's assume the number of students who solved more than one problem is "x". - (1/4) * x students correctly solved at least 3 problems. 3. Let's assume the number of students who solved at least 3 problems is "y". - (1/3) * y students correctly solved exactly 4 problems.

To find the number of students who correctly solved exactly one problem: - Total students who solved at least one problem: 20 students - Students who solved more than one problem: (1/4) * x - Students who solved at least 3 problems: y - Students who solved exactly 4 problems: (1/3) * y

The number of students who correctly solved exactly one problem can be calculated as: 20 - (1/4) * x - y

Let's solve for "x" and "y" using the given information.

Solution

1. 80% of 25 students = 20 students2. Let's assume the number of students who solved more than one problem is "x". - (1/4) * x students correctly solved at least 3 problems. - Therefore, (3/4) * x students solved exactly 2 problems or more. - Students who solved exactly 2 problems = (3/4) * x - (1/4) * x = (2/4) * x = (1/2) * x 3. Let's assume the number of students who solved at least 3 problems is "y". - (1/3) * y students correctly solved exactly 4 problems. - Therefore, (2/3) * y students solved exactly 3 problems. 4. Students who solved exactly one problem = Total students who solved at least one problem - Students who solved more than one problem - Students who solved at least 3 problems - Students who solved exactly one problem = 20 - (1/2) * x - (2/3) * y

Now, we need to solve for "x" and "y" using the given information.

Calculation

Let's solve for "x" and "y" using the given information.

1. 80% of 25 students = 20 students2. Among the students who solved more than one problem, one-fourth of them correctly solved at least 3 problems. - (1/4) * x = (3/4) * x - (1/4) * x - (1/4) * x = (2/4) * x = (1/2) * x 3. One-third of the students who solved at least 3 problems correctly solved exactly 4 problems. - (1/3) * y = (2/3) * y 4. Students who solved exactly one problem = 20 - (1/2) * x - (2/3) * y

We need more information to solve the problem.