Question 1142701
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Let "  n "  be the number of sheep.


Then from the condition you have this equation


    {{{9000/n}}} - {{{9000/(n+3)}}} = 100.


Divide by 100 both sides. You will get


    {{{90/n}}} - {{{90/(n+3)}}} = 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.


<U>ANSWER</U>.  15 sheep.


<U>CHECK</U>.   {{{9000/15}}} - {{{9000/(15+3)}}} = 600 - 500 = 100.    ! Correct !
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Solved.