Question

В первой главе учебника имеется 5 параграфов, каждый из которых содержит одинаковое количество задач. Полина правильно решила 20 задач. Процент решенных задач оказался больше 70, но меньше 90. Сколько задач в этой главе? Помогите пожалуйста

Answer 1

Number of Problems in the Chapter

To determine the number of problems in the chapter, we can use the information given in the question. We know that there are 5 paragraphs in the chapter, and each paragraph contains the same number of problems. Let's assume that the number of problems in each paragraph is x.

Since Polina correctly solved 20 problems, we can conclude that the percentage of problems she solved is greater than 70% but less than 90%.

To find the range of the number of problems in the chapter, we can set up the following inequality:

70% ≤ (20 / (5 * x)) * 100 < 90%

Simplifying the inequality, we get:

0.7 ≤ (20 / (5 * x)) < 0.9

To solve for x, we can multiply both sides of the inequality by 5 * x:

0.7 * (5 * x) ≤ 20 < 0.9 * (5 * x)

Simplifying further:

3.5 * x ≤ 20 < 4.5 * x

Now, we can solve the inequality to find the possible values of x:

3.5 * x ≤ 20

Dividing both sides by 3.5:

x ≤ 20 / 3.5

x ≤ 5.71

20 < 4.5 * x

Dividing both sides by 4.5:

20 / 4.5 < x

x > 4.44

Therefore, the number of problems in each paragraph is greater than 4.44 and less than or equal to 5.71.

Since the number of problems must be a whole number, we can conclude that the number of problems in each paragraph is 5.

To find the total number of problems in the chapter, we can multiply the number of paragraphs by the number of problems in each paragraph:

Total number of problems = 5 paragraphs * 5 problems per paragraph = 25 problems

So, there are 25 problems in this chapter.