SOLUTION: This is an algebra question :-) and thank you for helping in advance:D A bookshop owner bought x pencils for $32 and sold them at a profit of 5 cents per pencil. She ended up wi

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Question 1046951: This is an algebra question :-) and thank you for helping in advance:D
A bookshop owner bought x pencils for $32 and sold them at a profit of 5 cents per pencil. She ended up with 20 pencils left and received $35 for the sale of the pencils.
a)Find the selling price of each pencil
b)Form an equation in x and show that it reduces to x%5E2-80x-12800+=+0
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A bookshop owner bought x pencils for $32 and sold them at a profit of 5 cents per pencil.
She ended up with 20 pencils left and received $35 for the sale of the pencils.
a)Find the selling price of each pencil.
32%2Fx = price she paid for each pencil
thne
32%2Fx + .05 = selling price of the pencil
:
(x-20)*(32%2Fx+.05) = 35
:
(x-20)%28%2832%2B.05x%29%2Fx%29%29 = 35
multiply both sides by x
(x-20) (32 + .05x) = 35x
FOIL
32x + .05x^2 - 640 - x = 35x
arrange as a quadratic equation\
.05x^2 + 32x - x - 35x + 640 = 0
.05x^2 - 4x + 640 = 0
multiply eq by 20 to have a coefficient of 1 for x^2
x^2 - 80x + 12800 = 0
you can use the quadratic formula; a=1; b=-80; c=-12800
but this will factor to
(x+80)(x-160) = 0
positive solution
x = 160 pencils
:
Find the selling price:
32/160 = .20 price she paid
therefore
.25 selling price for each pencil