Question 1142701
he bought x number of sheep for 9000.
the price per sheep is y.
therefore x * y = 9000


if the price was 100 less, he could have bought 3 more sheep for the same money.
the equation for that becomes (x + 3) * (y - 100) = 9000


you have 2 equations that need to be solved simultaneously.
they are:


x * y = 9000
(x + 3) * (y - 100) = 9000


simplify these equations to get:


x * y = 9000
x * y - 100 * x + 3 * y - 300 = 9000


replace x * y in the second equation with 9000 from the first equation to get:


9000 - 100 * x + 3 * y - 300 = 9000


the 9000 on both sides of the equation cancel out and you are left with:


-100 * x + 3 * y - 300 = 0


from the first equation of x * y = 9000, solve for y to get y = 9000 / x


in the second equation of -100 * x + 3 * y - 300 = 0, replace y with 9000 / x to get:


-100 * x + 3 * (9000 / x) - 300 = 0
multiply both sides of this equation by x to get:
-100 * x^2 + 27000 - 300 * x = 0
reorder this equation in descending order of degree to get:
-100 * x^2 - 300 * x + 27000 = 0
divide both sides of this equation by -100 to get:
x^2 + 3x - 270 = 0
factor this equation to get (x + 18) * (x - 15) = 0
solve for x to get x = -18 or x = 15
x has to be positive, so x = 15 looks like a possible solution.


when x = 15, x * y = 9000 gets you y = 600.
you get:
x * y = 15 * 600 = 9000
(x + 3) * (y - 100) becomes 18 * 500 = 9000


solution is:
he bought 15 sheep at 600 apiece for a total cost of 9000.
if the price dropped 100 for each sheep, then he could have bought 18 sheep at 500 apiece for the same total cost of 9000.