Question 896704
x = number of shares he sold.
p = price per share he sold at.



you get x*p = 2880


price went down 2 and he bought back 6 more shares at the same total price.


you get (x+6) * (p-2) = 2880


since they both equal 2880, you can set x*p equal to (x+6)*(p-2).


your equation to solve is:


x*p = (x+6) * (p-2)


simplify this equation to get:


x*p = x*p - 2x + 6p - 12


subtract x*p from both sides of this equation to get:


0 = -2x + 6p - 12


from x*p = 2880, you can solve for p to get:


p = 2880 / x


replace p in the equation of 0 = -2x + 6p - 12 to get:


0 = -2x + 6(2880/x) - 12


multiply both sides of this equation by x to get:


0 = -2x^2 + 6*2880 - 12


simplify to get:


0 = -2x^2 + 17280 - 12x


divide both sides of this equation by -2 to get:


0 = x^2 - 8640 + 6x


rearrange the terms in descending order of degrees of x to get:


0 = x^2 + 6x - 8640


factor x^2 + 6x - 8640 to get:


0 = (x+96) * (x-90)


solve for x to get:


x = -96 or x = 90


since x has to be positive, your solution appears to be x = 90


when x = 90, p = 2880 / 90 = 32


he sold 90 shares at 32 dollars apiece to get 2880.


later he bought back 96 shares at 30 dollars apiece for a total cost of 2880.


numbers check out so your solution is:


he sold 90 shares.