Question

Помогите пожалуйста. Дмитрий прочитал книгу за 3 дня. В первый день он прочитал 30% и еще 4 страницы,во второй день-60% остатки и еще 14 страниц,в третий день-85% нового остатка и последние 9 страниц. Сколько страниц в книге???

Answer 1

Calculation of the Total Number of Pages in the Book

To calculate the total number of pages in the book, we need to add up the number of pages Dmitry read on each day.

- On the first day, Dmitry read 30% of the book and an additional 4 pages. - On the second day, he read 60% of the remaining pages and an additional 14 pages. - On the third day, he read 85% of the remaining pages and the final 9 pages.

Let's calculate the total number of pages in the book step by step:

1. Calculate the number of pages Dmitry read on the first day: - Let's assume the total number of pages in the book is x. - Dmitry read 30% of the book, which is 0.3x pages. - He also read an additional 4 pages. - So, the number of pages Dmitry read on the first day is 0.3x + 4.

2. Calculate the number of pages Dmitry read on the second day: - On the second day, Dmitry read 60% of the remaining pages. - The remaining pages after the first day are x - (0.3x + 4). - Dmitry read 60% of the remaining pages, which is 0.6 * (x - (0.3x + 4)) pages. - He also read an additional 14 pages. - So, the number of pages Dmitry read on the second day is 0.6 * (x - (0.3x + 4)) + 14.

3. Calculate the number of pages Dmitry read on the third day: - On the third day, Dmitry read 85% of the remaining pages. - The remaining pages after the second day are x - (0.3x + 4) - (0.6 * (x - (0.3x + 4)) + 14). - Dmitry read 85% of the remaining pages, which is 0.85 * (x - (0.3x + 4) - (0.6 * (x - (0.3x + 4)) + 14)) pages. - He also read the final 9 pages. - So, the number of pages Dmitry read on the third day is 0.85 * (x - (0.3x + 4) - (0.6 * (x - (0.3x + 4)) + 14)) + 9.

4. Calculate the total number of pages in the book: - The total number of pages in the book is the sum of the pages Dmitry read on each day. - So, we add up the pages from the first, second, and third days: 0.3x + 4 + 0.6 * (x - (0.3x + 4)) + 14 + 0.85 * (x - (0.3x + 4) - (0.6 * (x - (0.3x + 4)) + 14)) + 9.

Now, let's simplify the equation and solve for x, which represents the total number of pages in the book.

Solution:

To find the total number of pages in the book, we need to solve the equation:

0.3x + 4 + 0.6 * (x - (0.3x + 4)) + 14 + 0.85 * (x - (0.3x + 4) - (0.6 * (x - (0.3x + 4)) + 14)) + 9 = x

Simplifying the equation:

0.3x + 4 + 0.6x - 0.6(0.3x + 4) + 14 + 0.85x - 0.85(0.6x - 0.6(0.3x + 4) + 14) + 9 = x

0.3x + 4 + 0.6x - 0.18x - 0.6(4) + 14 + 0.85x - 0.51x + 0.51(0.3x + 4) - 0.51(14) + 9 = x

0.3x + 4 + 0.6x - 0.18x - 2.4 + 14 + 0.85x - 0.51x + 0.153x + 2.04 - 7.14 + 9 = x

1.32x + 20.5 = x

0.32x = -20.5

x = -20.5 / 0.32

x ≈ -64.06

Since the result is negative, it doesn't make sense in the context of the problem. It's possible that there was an error in the given information or calculation. Please double-check the values provided for each day's reading progress and try again.

If you have any further questions, feel free to ask!