Question

Собранение сочинений Конан Дойла содержит 5 толстых томов, 4 средних и 3 тонких тома. Количество страниц в среднем томе на 30 меньше, чем в толстом, и на 20 больше, чем в тонком. Сколько страниц в каждом томе, если общее число страниц в общем собрании 6090?

Answer 1

Х страницы в среднем томе
х+30 страницы в толстом
х-20 страницы в тонком
5(х+30)+4х+3(х-20)=6090
5х+150+4х+3х-60=6090
12х=6000
х=500 стр. средний том
500+30=530стр. толстый
500-20=480стр. тонкий

Answer 2

Problem Analysis

We are given the information that a collection of Conan Doyle's works consists of 5 thick volumes, 4 medium volumes, and 3 thin volumes. We are also given that the number of pages in a medium volume is 30 less than the number of pages in a thick volume, and 20 more than the number of pages in a thin volume. We need to determine the number of pages in each volume if the total number of pages in the entire collection is 6090.

Solution

Let's assume the number of pages in a thick volume is x.

According to the given information, the number of pages in a medium volume is 30 less than the number of pages in a thick volume. Therefore, the number of pages in a medium volume is x - 30.

Similarly, the number of pages in a thin volume is 20 less than the number of pages in a medium volume. Therefore, the number of pages in a thin volume is (x - 30) - 20, which simplifies to x - 50.

Now, we can calculate the total number of pages in the entire collection by multiplying the number of pages in each type of volume by the number of volumes of that type and adding them together:

Total number of pages = (5 * x) + (4 * (x - 30)) + (3 * (x - 50))

We know that the total number of pages in the entire collection is 6090. So we can set up the equation:

(5 * x) + (4 * (x - 30)) + (3 * (x - 50)) = 6090

Now, let's solve this equation to find the value of x.

Calculation

(5 * x) + (4 * (x - 30)) + (3 * (x - 50)) = 6090

Simplifying the equation:

5x + 4x - 120 + 3x - 150 = 6090

12x - 270 = 6090

12x = 6360

x = 6360 / 12

x = 530

Answer

Therefore, the number of pages in a thick volume is 530.

Using this information, we can calculate the number of pages in a medium volume and a thin volume:

Number of pages in a medium volume = 530 - 30 = 500

Number of pages in a thin volume = 500 - 20 = 480

So, the number of pages in each volume is as follows: - Thick volume: 530 pages - Medium volume: 500 pages - Thin volume: 480 pages

Please let me know if I can help you with anything else.