Warren read 1/6 of the pages of a book last Monday. Tuesday here at 2/5 the remaining pages.How many pages does the book have?.

Question

* please read*

Warren read 1/6 of the pages of a book last Monday. Tuesday here at 2/5 the remaining 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?.

 

Please explain the steps that should be taken to write the equation etc. I am trying to get used to identifying what I am looking for, setting up my equation, and then solving. I believe taking these steps will help me far more in the long run.

Answer 1

Here's what we know:

¹/₆ + ²/₅ + x = 1 (the fractions read plus the 60 pages (currently an unknown fraction) makes one whole book)

 

First we need a common denominator. LCD is 30:

⁵/₃₀ + ¹²/₃₀ + x = 1

¹⁸/₃₀ + x = 1

Subtract:

x = ³⁰/₃₀ - ¹⁸/₃₀

x = ¹²/₃₀

 

Now we have an equivalency. 60 pages out of the whole book is equal to 12/30. Or:

⁶⁰/_y = ¹²/₃₀

Cross multiply:

60 * 30 = 12y

Divide both sides by 12:

60 * 30 / 12 = y

Factor out a 6:

10 * 30 / 2 = y

Factor out 2:

10 * 15 = y

150 = y

 

There are 150 pages in the book.