Question 1154580
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Let n be the number of pencils under the problem's question.


The the owner bought n pencils for 32 dollars at the price  {{{3200/n}}}  cents per dollar.


Then the owner sold (n-20) pencils for 35 dollars, at the price  {{{3500/(n-20)}}}  cents per pencil.


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


It gives you an equation


    {{{3500/(n-20)}}} - {{{3200/n}}} = 5  cents.


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


Cancel the factor 5 in both sides


    {{{700/(n-20)}}} - {{{640/n}}} = 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).


<U>ANSWER</U>.  n= 160.


<U>CHECK</U>.  I will check equation (*):  {{{700/(160-20)}}} - {{{640/160}}} = 5 - 4 = 1.    ! Precisely correct !
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Solved.