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
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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):
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.
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 !
