SOLUTION: A man bought some materials for a total amount of 90000. If he had bought 50 more materials, it would have cost him 20 less per piece. how many materials did he buy?

Question 466692: A man bought some materials for a total amount of 90000. If he had bought 50 more materials, it would have cost him 20 less per piece. how many materials did he buy?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A man bought some materials for a total amount of 90000.
If he had bought 50 more materials, it would have cost him 20 less per piece.
how many materials did he buy?
:
Let p = original price for each
Let x = original no. of items purchased
:
p*x = 90000
p =
:
"If he had bought 50 more materials, it would have cost him 20 less per piece."
(p-20)*(x+50) = 90000
FOIL
px + 50p - 20x - 1000 = 90000
:
we know px = 90000, so we have
90000 + 50p - 20x - 1000 = 90000
:
subtract 90000 from both sides
50p - 20x - 1000 = 0
:
simplify, divide by 10
5p - 2x - 100 = 0
:
Replace p with
5(90000/x) - 2x - 100 = 0
(450000/x) - 2x - 100 = 0
multiply by x
450000 - 2x^2 - 100x = 0
Arrange as a quadratic equation we can factor, multiply by -1
2x^2 + 100x - 450000 = 0
This factors to
(2x - 900) (x + 500) = 0
Positive solution
2x = 900
x = 450 units originally purchased
:
:
Check this out, find the original cost per unit
= $200
How many could he get if he paid $20 less, $180?
= 500 unit which is 50 units more

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