SOLUTION: Hi A bookstore owner bought x pencils for 32 dollars and sold them at a profit of 5 cents per pencil. She ended up with 20 pencils left and received 35 dollars for the sale of t

Let n be the number of pencils under the problem's question.


The the owner bought n pencils for 32 dollars at the price    cents per dollar.


Then the owner sold (n-20) pencils for 35 dollars, at the price    cents per pencil.


The difference in prices per pencil was 5 cents, according to the condition.


It gives you an equation


     -  = 5  cents.


It is your basic equation to solve and to find the unknown "n".


Cancel the factor 5 in both sides


     -  = 1.     (*)


To solve this equation, multiply both sides by n*(n-20) and reduce the equation to standard quadratic equation form;

then solve it by any method you know / (by any method you can).


ANSWER.  n= 160.


CHECK.  I will check equation (*):   -  = 5 - 4 = 1.    ! Precisely correct !