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Answer to Question #3272 in Algebra for David Mugo

Question #3272
A retailer bought a number of pens at 180sh he sold all butt 6 at a profit of 2sh per pen. <br>If he used all the amount he received to buy pens he will buy 30 more pens then what he bought initially find the cost of one pen?
Expert's answer
Let N be the total number of pens bought by retailer, and P be the price for the one.
Then
NP = 180
Then he sold N-6 pens at price P+2.
The profit is equal to
(N-6)(P+2) - NP = 2N - 6P - 12
and for this money the retailer can bought 30 pens.
So
2N - 6P - 12 = 30 P
whence
N = 18 P + 6
Substituting this expression to the initial formula NP=180
we get
18 P2 + 6P - 180 = 0
or
3P2 + P - 30 = 0
Solving this quadratic equation we get the following
P=3 or P = -10/3.

Thus P=3, and N=180/3=60.

Answer.
The cost of one pen is 3 sh.

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