Question 1123893
let x equal the number of shares bought.
let p = the price per share they were bought at.
let x-15 equal the number of shares sold.
let p+4 equal the price per share they were sold at.


he bought them for 1875.
he sold 15 less for 1740 at a profit of 4 each.


your equations are:


xp = 1875
(x-15) * (p+4) = 1740


these euations need to be solved simultaneously.


simplify the equations to get:


xp = 1875
xp + 4x - 15p - 60 = 1740


add 60 to both sides of the second equation and leave the first equation as is to get:


xp = 1875
xp + 4x - 15p = 1800


subtract the first equation from the second to get:


4x - 15p = -75


add 75 to both sides of this equation to get:


4x - 15p + 75 = 0


from the first original equation of xp = 1875, solve for p to get:


p = 1875/x


in the last equation of 4x - 15p + 75 = 0, replace p qith 1875/x to get:


4x - 15*1875/x + 75 = 0


multiply both sides of this equation by x to get:


4x^2 - 15*1875 + 75x = 0


simplify to get:


4x^2 - 28125 + 75x = 0


reorder the terms in descending order of degree to get:


4x^2 + 75x - 28125 = 0


factor this quadratic equation to get:


x = -93.75 or x = 75


x can't be negative, so x = 75 or not at all.


when x = 75, .....


xp = 1875 becomes 75p = 1875.
solve for p to get p = 1875/75 = 25.


when x = 75 and p = 25, .....


(x-15) * (p+4) = 1740 becomes 60 * 29 = 1740 which becomes 1740 = 1740, confirming the solution is correct.


the solution is that he bought 75 shares.