How many pages are in the book?

Question

On the first day a boy reads one third and 5 pages of a book. On the second day he reads 11 pages less than the two thirds of the remaining pages. By the third day one fourth of the book remains. How many pages are in the book.

The answer is 336 pages, but I would like to know the steps to get to the answer.

Answer 1

Let x = #pages in the book

On day 1 the number of read pages is x/3 + 5.

Getting ready for day 2 the number of remaining pages is x - (x/3 + 5) = 2x/3 - 5.

On day 2 she read 11 less than 2/3 of the remaining pages: 2/3[2x/3 - 5] - 11= 4x/9 - 10/3 -33/3 =

4x/9 - 43/3.

Since 1/4 of the book remains to be read, that means 3/4 of the book has been read. So the number of pages read on day 1 plus number of pages read on day 2 must equal 3x/4.

x/3 + 5 + 4x/9 - 43/3 = 3x/4 (multiply every term of this equation by 36 to clear the fractions)

12x + 180 + 16x - 516 = 27x

28x - 336 = 27x

x = 336

Day 1: 112+5 = 117 (pages remaining = 336 - 117 = 219)

Day 2: 2/3 of 219 - 11 = 135 (pages read so far is 117 + 135 = 252, so pages remaining = 336 - 252 = 84)

Day 3: 1/4 of 336 = 84