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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