Algebraic Word Problem

[nem11]

'A 120-page book has p lines to a page. If the number of lines was reduced by three on each page, the number of pages would need to be increased by 20 to give the same amount of writing space. How many lines were there on the page originally?'

A I have a fair idea that in order to solve this I need to construct an equation and then solve from there. However, consturcting the right equation is what I'm having trouble with!

 

[Deleted member 4993]

'A 120-page book has p lines to a page. If the number of lines was reduced by three on each page, the number of pages would need to be increased by 20 to give the same amount of writing space. How many lines were there on the page originally?'

A I have a fair idea that in order to solve this I need to construct an equation and then solve from there. However, consturcting the right equation is what I'm having trouble with!

Start giving names to unknown to be found.

Let the number of lines per page = n

Then there are 120*n number of lines in the book.

If we reduce number of lines per page by 3 - we get

number of lines per page = n -3

Then the number of pages increase to 140.

Now what....

 

[nem11]

Thank-you very much! So it would be:

140(n-3)=120n

140n - 420 = 120n

140n - 120n = 420

20n = 420

n = 420/20

n = 21

 

[Deleted member 4993]

Looks good to me......