SOLUTION: The problem: A library receives a large cash donation and uses the funds to double the number of books it owns. Then a book collector gives the library 4028 books. After this, the

Algebra ->  Customizable Word Problem Solvers  -> Evaluation -> SOLUTION: The problem: A library receives a large cash donation and uses the funds to double the number of books it owns. Then a book collector gives the library 4028 books. After this, the      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 677885: The problem:
A library receives a large cash donation and uses the funds to double the number of books it owns. Then a book collector gives the library 4028 books. After this, the library has 51,514 books. How many books did the library have before the cash donation and the gift of books?
I've been trying so many different ways to solve this and I can't figure out how you would find out many books they had originally. I needed to define a variable and write an equation for the situation then solve it. I'm very confused can someone please explain this to me?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
the library started with an unknown +x+ number of books
The cash donation allowed them to double that number, so
then they had +2x+ books
Then a book collector gave the library 4028 books, so then
they had +2x+%2B+4028+ books
The total after that was +51514+ books, so
+2x+%2B+4028+=+51514+
+2x+=+51514+-+4028+
+2x+=+47486+
+x+=+23743+
The library started with 23,743 books