Warren read 1/6 of the pages of a book last Monday. Tuesday he read 2/5 of the remainder of the pages. Wednesday he read 1/3 of the remaining pages. He has 60 more pages left to read. How many pages does the book have?
Total = X pages.
Monday: 1/6 * x = x/6 Pages read.
x-x/6 = 6x/6 - x/6 = 5x/6 Remaining.
Tuesday: 2/5 * 5x/6 = x/3 Pages read.
5x/6 - x/3 = 5x/6 - 2x/6 = 3x/6 Remaining.
Wednesday: 1/3 * 3x/6 = x/6 Pages
read.
3x/6 - x/6 = 2x/6 = x/3 Remaining.
x/3 = 60, X = 180 Pages.
To solve this problem, we can break it down into smaller steps.
1. Let's start by finding out how many pages Warren read on Tuesday. Since he read 1/6 of the book on Monday, the remaining pages would be 1 - 1/6 = 5/6 of the book.
Warren read 2/5 of the remainder, so the number of pages read on Tuesday would be (2/5) * (5/6) of the book.
Calculating the multiplication, we find that Warren read (2/5) * (5/6) = 2/6 = 1/3 of the book on Tuesday.
2. Next, let's find out how many pages Warren read on Wednesday. The remaining pages after Tuesday would be (5/6) - (1/3) = (5/6) - (2/6) = 3/6 = 1/2 of the book.
Warren read 1/3 of the remaining pages, so the number of pages read on Wednesday would be (1/3) * (1/2) of the book.
Calculating the multiplication, we find that Warren read (1/3) * (1/2) = 1/6 of the book on Wednesday.
3. Now let's find out how many pages are left after Wednesday. The remaining pages after Wednesday would be (1/2) - (1/6) = (3/6) - (1/6) = 2/6 = 1/3 of the book.
We are given that there are 60 pages left to read, which is equal to 1/3 of the book. So we can set up the equation:
(1/3) * x = 60
Solve for x (the total number of pages) by multiplying both sides of the equation by the reciprocal of 1/3, which is 3/1:
x = 60 * (3/1) = 180.
Therefore, the book has 180 pages.