SOLUTION: A speculator sold some shares of stock for $2880. Several days later, the stock having dropped in price $2 per share, he repurchased, for the same amount of money, 6 more shares th

Question 896704: A speculator sold some shares of stock for $2880. Several days later, the stock having dropped in price $2 per share, he repurchased, for the same amount of money, 6 more shares than he sold. How many shares did he sell?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

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