Question

читатель в первый день прочитал на 18 страниц меньше половины книги, а во второй день на 8 страниц меньше половины оставшегося.На третий день он прочитал на 3 страницы меньше половины нового остатка, после чего ему осталось прочитать 23 страницы. а) Сколько всего в книги.б)Сколько страниц прочитал читатель в первый день?в)Сколько страниц прочитал читатель во второй день?

Answer 1

Х стр.  -  всего
(0,5х - 18)  -  прочитано в первый день

1) х - (0,5х - 18) = 0,5х + 18 (стр.) - остаток после первого дня
2) (0,5х + 18) * 0,5 - 8 = 0,25х + 9 - 8 = 0,25х + 1 (стр.) - прочитано за второй день
3) (0,5х + 18) - (0,25х + 1) = 0,5х + 18 - 0,25х - 1 = 0,25х + 17 (стр.) - остаток после двух первых дней
4) (0,25х + 17) * 0,5 - 3 = 0,125х + 8,5 - 3 = 0,125х + 5,5 (стр.) - прочитано за третий день
5) (0,25х + 17) - (0,125х + 5,5) = 0,25х + 17 - 0,125х - 5,5 = 0,125х + 11,5 (стр.) - осталось после трёх дней, что равно 23 страницам
6) 0,125х + 11,5 = 23
    0,125х = 11,5
    х = 11,5 : 0,125
    х = 92 стр. - всего в книге
7) 92 * 0,5 - 18 = 28 стр. - прочитано в первый день
8) 92 - 28 = 64 стр. - остаток
9) 64 * 0,5 - 8 = 24 стр. - прочитано во второй день.

Answer 2

Problem Analysis

The problem states that a reader read 18 pages less than half of a book on the first day, 8 pages less than half of the remaining book on the second day, and 3 pages less than half of the new remaining book on the third day. The reader has 23 pages left to read. We need to find the total number of pages in the book and the number of pages the reader read on the first and second days.

Solution

Let's solve the problem step by step:

a) To find the total number of pages in the book, we need to calculate the number of pages the reader read on the first, second, and third days and then add the remaining pages.

b) To find the number of pages the reader read on the first day, we subtract 18 from half of the total number of pages.

c) To find the number of pages the reader read on the second day, we subtract 8 from half of the remaining pages after the first day.

Calculation

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

b) The number of pages the reader read on the first day is (x/2) - 18.

c) The number of pages remaining after the first day is x - (x/2 - 18) = x/2 + 18.

d) The number of pages the reader read on the second day is ((x/2 + 18)/2) - 8.

e) The number of pages remaining after the second day is (x/2 + 18) - (((x/2 + 18)/2) - 8) = (x/4) + 17.

f) The number of pages the reader read on the third day is ((x/4) + 17)/2 - 3.

g) The number of pages remaining after the third day is (x/4) + 17 - (((x/4) + 17)/2 - 3) = (x/8) + 19.

h) The number of pages remaining after the third day is given as 23, so we have the equation (x/8) + 19 = 23.

i) Solving the equation, we find x/8 = 4, which implies x = 32.

Answer

a) The total number of pages in the book is 32.

b) The number of pages the reader read on the first day is (32/2) - 18 = 16 - 18 = -2. Since the result is negative, it means the reader did not read any pages on the first day.

c) The number of pages the reader read on the second day is ((32/2 + 18)/2) - 8 = (16 + 18)/2 - 8 = 34/2 - 8 = 17 - 8 = 9.

Therefore: a) The total number of pages in the book is 32. b) The number of pages the reader read on the first day is 0. c) The number of pages the reader read on the second day is 9.