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

Question 1154580: 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 the pencils.
How many pencils did he buy.
Thanks
Found 2 solutions by ikleyn, mananth:
Answer by ikleyn(52788) (Show Source): You can put this solution on YOUR website!
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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 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 !

Solved.

Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
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 the pencils.
How many pencils did he buy.
each pencil costs 32/x dollars
sold at ((32/x) +0.05) $
(x-20)((32/x) +0.05)=35
32-640/x +0.05x -1=35
-640/x +0.05x =4
-640 +0.05x^2 =4x
0.05x^2-4x-640=0
multiply by 100
5x^2-400x-64000=0
x^2-80x -12800=0
(x+80)(x-160)=0
x=-80 or x =160
Number of pencils cannot be negative

pencils bought =160

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