SOLUTION: John bought a number of notepads for $70. Four of the notepads got spoiled. He sold the remaining notepads at $3 more per pad than he paid, and made a total profit of $10. How many

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Question 619064: John bought a number of notepads for $70. Four of the notepads got spoiled. He sold the remaining notepads at $3 more per pad than he paid, and made a total profit of $10. How many notepads did John buy?
Found 2 solutions by ankor@dixie-net.com, ewatrrr:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
John bought a number of notepads for $70.
Four of the notepads got spoiled.
He sold the remaining notepads at $3 more per pad than he paid, and made a total profit of $10.
How many notepads did John buy?
:
Let n = number of pads he bought
then
(n-4) = number of pads sold
:
70%2Fn = original cost for each pad
:
70%2Fn + 3 = selling price of the each pad
:
Revenue - cost = $10
(n-4)*(70%2Fn + 3) - 70 = 10
(n-4)*(70%2Fn + 3) = 80
%2870%28n-4%29%29%2Fn + 3(n-4) = 80
%2870n-280%29%2Fn + 3n - 12 = 80
%2870n-280%29%2Fn + 3n = 92
multiply by n
70n - 280 + 3n^2 = 92n
Arrange as a quadratic equation
3n^2 + 70n - 92n - 280 = 0
3n^2 - 22n - 280 = 0
you can use the quadratic formula, but this will factor to
(3n + 20)(n - 14) = 0
Positive solution
n = 14 note pads originally bought
:
:
See if that checks out
70/14 = $5 original cost
then
5 + 3 = $8 selling price
:
10* 8 = $80 revenue, (4 less sold)
cost: = $70
------------
profit: $10

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

John bought a numberhighlight%28x%29 of notepads for $70. $70/x per pad Four of the notepads got spoiled. 

He sold the remaining notepads at $3 more per pad than he paid, and made a total profit of $10. 

How many notepads did John buy?

 +%28x-4%29%2A%28%2870%2Fx%29+%2B3%29+-70+=+10 ****

+70%28x-4%29%2Fx+%2B+3%28x-4%29+=+80+   |||Multiplying thru by x so as all denominators = 1

  70(x-4) + 3x(x-4) = 80x

   3x^2 + 58x -200 = 80x

   3x^2 -22x  - 280 = 0

x+=+%2822+%2B-+sqrt%28+3844+%29%29%2F%286%29+

x+=+%2822+%2B-+62%29%2F%286%29+

   x = 14, throwing out the negative solution for count

CHECKING our Answer***  70/14 = $5 pd for the notepads originally

  10· $8 - $70 = $10