# Algebra word problem

### Algebra word problem

Hello,

First off, I'd like to congratulate you guys for the awesome website.

I got a question regarding one word problem that has the following statement:

"Kamen read 2/3 of a book. He calculated that he read 90 pages more than the rest of it. How many pages does the book have?"

As you noticed, 2/3x is equal to 90 pages. Therefore, "x" is the total amount of pages the book has.

2/3x=90 => x=90/2/3=> x=135

To my surprise and dispair, the answer was 270. Below is the solution:

"If denote the total number pages by x, then he read 2/3.x
x-2/3.x=1/3.x is number of the rest of the book.
2/3.x-1/3.x=90 => 1/3.x=90 => x=270
So the book has 270 pages."

Edielton
Guest

### Re: Algebra word problem

Are you saying you do not understand the solution provided as well.? ? ?.

If that is the case I will add some notes........

Assume the QUESTION is correct.....He has read 2/3 of the book, so that means 1/3 still to read. There are three thirds in 1 whole.
He has counted the pages and knows there are 90 more pages in the 2/3 he has read than there are in the 1/3 he has still to read.

Your reasoning is wrong at this point.....You state...."As you noticed, 2/3x is equal to 90 pages." No the question does not tell you that.
It tells you there are 90 MORE pages in the 2/3 bit that is read. So your calculation is wrong.

The solution provided in the last post is correct.....

It Lets X = number of pages in the book.

So 2/3 of X is read......2/3.x

And (x - (2/3.x)) = (1/3.x) still to read.

From the question we know ( what was read is 90 pages more that what is still to read )

So...... (what was read (2/3.x) minus 90 pages would equal what is left to read)

So........( 2/3.x) - 90 = (1/3.x)

Rearranging (2/3.x) - (1/3.x) = 90 .....same as saying "what was read" minus "what is still to read" equals "90 pages"....

So 1/3.x = 90

So multiply across by 3 .... x = 270 pages in whole book.
Guest