Michael purchased a certain number of shares of one stock fo

Michael purchased a certain number of shares of one stock for a total of $1287. The second stock was selling for $6 less per share. Michael could have bought 6 more shares of the second stock for the same amount of money. How many shares of the first stock did Michael purchase ? How much did each share cost?

Solution

Let, x be cost of first stock\'s share

SO number of shres of first stock bought =1287/x

Second stock costs: x-6

So number of shares of second stock that can be bought =1287/(x-6)

So,

1287/x+6=1287/(x-6)

1287(x-6)+6x(x-6)=1287x

6x^2-36x-1287*6=0

x^2-6x-1287=0

1287=429*3=143*9=13*11*9=39*33

x^2-39x+33x-1287=0

x(x-39)+33(x-39)

=0

x=39

So first share costs 39 and second share costs 33

Number of shares of first stock purchased=1287/39=33