Question

Петя взял у Лены книгу на три дня. В первый день он прочитал полкниги, во второй-треть оставшихся страниц, а в третий день-количество страниц, равное половине страниц, прочитанных за первые два дня. Успел ли Петя прочитать за три дня книгу?

Answer 1

1)   1 - 1/2=1/2(часть) - осталось после первого дня
2)   1/2*1/3=1/6(часть) - прочитал во второй день
3)   (1/2+1/6) :2=1/3(часть) - прочитал в третий день
4)   1/2+1/6+1/3=6/6=1(часть) - прочитал за три дня.
Да, успел прочитать.

Answer 2

Problem Analysis

We are given that Petya borrowed a book from Lena for three days. On the first day, he read half of the book. On the second day, he read one-third of the remaining pages. And on the third day, he read a number of pages equal to half of the pages he read on the first two days. We need to determine if Petya managed to finish reading the book within the three-day period.

Solution

To solve this problem, we need to calculate the total number of pages in the book and compare it to the number of pages Petya read in three days.

Let's assume the total number of pages in the book is x.

On the first day, Petya read 1/2 of the book, which is x/2 pages.

On the second day, he read 1/3 of the remaining pages. The remaining pages after the first day are x/2 - x/6 = x/3. Therefore, on the second day, Petya read 1/3 of x/3, which is x/9 pages.

On the third day, Petya read a number of pages equal to half of the pages he read on the first two days. The total number of pages he read on the first two days is x/2 + x/9 = 5x/9. Therefore, on the third day, Petya read 1/2 of 5x/9, which is 5x/18 pages.

To determine if Petya managed to finish reading the book within three days, we need to calculate the total number of pages he read in three days and compare it to the total number of pages in the book.

The total number of pages Petya read in three days is x/2 + x/9 + 5x/18 = 9x/18 + 2x/18 + 5x/18 = 16x/18 = 8x/9.

If 8x/9 is equal to or greater than x, then Petya managed to finish reading the book within three days.

Let's calculate:

8x/9 >= x

Multiplying both sides by 9:

8x >= 9x

Subtracting 9x from both sides:

0 >= x

Since the number of pages in a book cannot be negative, we can conclude that Petya did not manage to finish reading the book within three days.

Therefore, the answer is No, Petya did not manage to read the book in three days.

Answer

No, Petya did not manage to read the book in three days.