Answer to Question #3272 in Algebra for David Mugo

Question

A retailer bought a number of pens at 180sh he sold all butt 6 at a profit of 2sh per pen.
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?

Answer 1

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.