Question

Девять учеников пятого класса решали задачи. Первый ученик решил одну задачу и одну десятую оставшихся.Второй ученик решил две задачи и одну десятую оставшихся т.д. Девятый ученик решил девять задач и одну десятую оставшихся. Оказалось что все ребята решили одинаковое количество задач и все задачи были решены. Сколько всего было задач.

Answer 1

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Answer 2

Problem Analysis

In this problem, there are nine students in the fifth grade who are solving math problems. The first student solves one problem and one-tenth of the remaining problems. The second student solves two problems and one-tenth of the remaining problems, and so on. It is mentioned that all the students solve the same number of problems, and all the problems are solved. We need to determine the total number of problems.

Solution

Let's assume that the total number of problems is x.

According to the given information, the first student solves one problem and one-tenth of the remaining problems. This can be expressed as:

1 + (1/10)(x - 1) = x/9

Simplifying the equation:

1 + (x - 1)/10 = x/9

Multiplying both sides of the equation by 90 to eliminate the denominators:

90 + 9(x - 1) = 10x

90 + 9x - 9 = 10x

90 - 9 = 10x - 9x

81 = x

Therefore, the total number of problems is 81.

Answer

The total number of problems was 81.