Math reading

Question

Tanya has read 390 page of a book, which is 75% of the book. How many pages are in his entire book?

Answer 1

It is good to learn to translate word (story) phrases into concise, precise math expressions.

 

Let:

   x = number of pages in the entire book

 

Translate:

  "Tanya has read 390 page of a book, which is 75% of the book"       means

                            390                                  =  75%   *       x

  "How many pages are in his entire book?"   means     report x

 

The math:

     390 = (3/4)x       [note:  75% = 75/100 = 0.75 =  3/4    as needed]

      520  = x        [multiply both sides by 4/3]

 

The entire book has 520 pages.

Answer 2

Since 390 is 75% of the book, you can set up the following equation:

 

0.75X = 390

where X represents the total number of pages in the book and 75% is re-written in decimal form

 

Now solve for X by dividing both sides by 0.75 (using a calculator). 390/0.75 = 520. 

 

If you do not have a calculator, you can convert 75% into fraction form, which is 3/4. Then divide 390/(3/4). Remember that when dividing by a fraction, you multiply by the reciprocal.

 

390 * (4/3) = 1560/3 = 520