SOLUTION: A farmer bought some sheep for Rs. 9000. If he had paid Rs. 100 less for each, he would have got 3 sheep more for the same money. How many sheep did he buy, when the rate in each c

Question 1142701: A farmer bought some sheep for Rs. 9000. If he had paid Rs. 100 less for each, he would have got 3 sheep more for the same money. How many sheep did he buy, when the rate in each case is same
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

Answer by ikleyn(52780) (Show Source): You can put this solution on YOUR website!
.

Let " n " be the number of sheep. Then from the condition you have this equation - = 100. Divide by 100 both sides. You will get - = 1. At this point, I just see a mental solution: n= 15. If you want to get a formal algebra solution, multiply both sides of the last equation by n*(n+3) and then simplify 90*(n+3) - 90n = n*(n+3) 90n + 270 - 90n = n^2 + 3n n^2 + 3n - 270 = 0 (n-15)*(n+18) = 0. Of the two roots n=15 and n= -18, only positive 15 is the solution to the problem. ANSWER. 15 sheep. CHECK. - = 600 - 500 = 100. ! Correct !

Solved.

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