Answer to Question #3272 in Algebra for David Mugo
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?
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.