SOLUTION: A farmer bought some sheep for $2100. Two sheep died, and he sold the rest for $30 more a head than he paid for them. If he made a profit of $60, how many sheep did he buy?

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Question 1116863: A farmer bought some sheep for $2100. Two sheep died, and he sold the rest for $30 more a head than he paid for them. If he made a profit of $60, how many sheep did he buy?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
A farmer bought some sheep for $2100. Two sheep died, and he sold the rest for $30 more a head than he paid for them.
If he made a profit of $60, how many sheep did he buy?
~~~~~~~~~~~~~~~~~~~~~~~ 

Let n be the number of sheep he bought.

Then he paid  2100%2Fn dollars for each.     (*)


Later he sold  (n-2) sheep  for 2100 + 60 = 2160 dollars,  and we know that  2160%2F%28n-2%29  is 30 dollars more than (*).


It gives you an equation

2160%2F%28n-2%29 - 2100%2Fn = 30.


Divide both sides by 30 to simplify. You will get

72%2F%28n-2%29 - 70%2Fn = 1.


Multiply both sides by n*(n-2). You will get


    72n - 70*(n-2) = n*(n-2)

    2n + 140 = n^2 - 2n

    n^2 - 4n - 140 = 0


    (n-14)*(n+10) = 0


The solution is  n = 14  sheeps.


Answer.   14 sheeps were originally.

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Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The solution by tutor ikleyn is fine.

Here is a different path which leads to the same equation to solve and of course the same answer.

Always be open to trying different methods for solving problems to find what methods "work" best for you.

If the original number of sheep is n, then the cost for each one was 2100/n.

Two of the sheep died, so the number he sold was (n-2).

He sold them for $30 more a head than he paid for them; so the selling price was (2100/n+30).

Selling (n-2) sheep for that price made him a profit of $60, so he sold them for a total of $2160.

So

%282100%2Fn%2B30%29%28n-2%29+=+2160
2100-4200%2Fn%2B30n-60+=+2160
30n-4200%2Fn+=+120
n-140%2Fn=4
n-4-140%2Fn=0
n%5E2-4n-140=0
%28n-14%29%28n%2B10%29+=+0
n+=+14

The number of sheep he bought was n=14.