# 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 P

or

3P

Solving this quadratic equation we get the following

P=3 or P = -10/3.

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

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 P

^{2}+ 6P - 180 = 0or

3P

^{2}+ P - 30 = 0Solving 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.The cost of one pen is 3 sh.

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