Question

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

Answer 1

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 also know that the number of pages in a medium volume is 30 pages less than a thick volume and 20 pages more than a thin volume. We need to determine the number of pages in each volume given that the entire collection contains 6,090 pages.

Solution

Let's denote the number of pages in a thick volume as T, the number of pages in a medium volume as M, and the number of pages in a thin volume as S.

From the given information, we can set up the following equations:

1. The total number of pages in the collection is 6,090: 5T + 4M + 3S = 6,090.

2. The number of pages in a medium volume is 30 pages less than a thick volume: M = T - 30.

3. The number of pages in a medium volume is 20 pages more than a thin volume: M = S + 20.

We can solve this system of equations to find the values of T, M, and S.

Solving the Equations

Let's substitute equation 2 into equation 3 to eliminate M:

T - 30 = S + 20.

Rearranging this equation, we get:

T - S = 50.

Now, we can substitute this equation into equation 1 to eliminate S:

5T + 4M + 3(T - 50) = 6,090.

Simplifying this equation, we get:

8T + 4M = 6,240.

Now, we can substitute equation 2 into this equation to eliminate M:

8T + 4(T - 30) = 6,240.

Simplifying this equation, we get:

12T = 6,480.

Dividing both sides of the equation by 12, we find:

T = 540.

Substituting this value back into equation 2, we can find M:

M = 540 - 30 = 510.

Finally, substituting the values of T and M into equation 1, we can find S:

5(540) + 4(510) + 3S = 6,090.

Simplifying this equation, we get:

2,700 + 2,040 + 3S = 6,090.

Combining like terms, we have:

3S = 1,350.

Dividing both sides of the equation by 3, we find:

S = 450.

Answer

Therefore, the number of pages in each volume is as follows: - Thick volume: 540 pages - Medium volume: 510 pages - Thin volume: 450 pages.

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