Question 824918
Of the animal on a farm 60% are cows and the rest are sheep. When 260 more cows and sheep are added to the farm, the percent of cows increases by 20% and the number of sheep doubles. Find the number of sheep originally on the farm.
<pre>
Let x = the number of animals originally on farm
</pre>
Of the animal on a farm 60% are cows...
<pre>
Then, since 60% = 0.6
0.6x = the number of cows originally on the farm
</pre>
and the rest are sheep.
<pre>
so the other 100%-60%=40% are sheep, and since 40% = 0.4

0.4x = the number of sheep originally on the farm
</pre>
When...more cows and sheep are added to the farm...the number of sheep doubles
<pre>
So the same number of sheep were added as were originally on the farm,
therefore,

0.4x = the number of sheep added
</pre>
260 more cows and sheep are added to the farm
<pre>
cows added = 260-sheep added = 260-0.4x

x+260 = the new number of animals on the farm
</pre>
the percent of cows increases by 20%
<pre><font color="red"><b>
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The word "percent" here should be "number".  For if you take what
is written literally, it would mean that after the 260 animals are 
added, then 60%+20%=80% of the animals are cows.  That interpretation 
will not work!  For if that were the case, then

   (original number of cows) + (cows added) = 80% of (new number of animals)    
                          0.6x + (260-0.4x) = 0.8(x+20)
                              0.6x+260-0.4x = 0.8x+16
                                   0.2x+260 = 0.8x+16
                                        244 = 0.6x
                                     406.67 = x
But the number of animals originally on the farm cannot be a fraction.
So I will change the wording to the only thing that could be meant:
----------------------------------------------------</font></b>

the NUMBER of cows increases by 20% (not <I>"the <u>percent</u> of cows increases by 20%"</I>!)

             {{{(matrix(8,1,
             the,number,of,cows,originally,on,the,farm))}}}{{{""+""}}}{{{(matrix(5,1,
             the,number,of,cows,added))}}} {{{""=""}}} {{{(matrix(8,1,
             the,number,of,cows,originally,on,the,farm))}}}{{{""+""}}}{{{(matrix(10,1,
            "20%",of,the,number,of,cows,originally,on,the,farm))}}} 

            0.6x + (260-0.4x) = 0.6x + 0.2(0.6x)
            0.6x+260-0.4x = 0.6x+0.12x
                 0.2x+260 = 0.6x+0.12x
                 0.2x+260 = 0.72x
                      260 = 0.52x
                     {{{260/0.52}}} = x
                      500 = x

So the farm originally contained 500 animals
0.6x = the number of cows originally on the farm = 0.6(500) = 300 cows
0.4x = the number of sheep originally on the farm = 0.4(500) = 200 sheep
0.4x = the number of sheep added = 200 sheep added
260-0.4x = the number of cows added = 260-200 = 60 cows added
x+260 = the new number of animals on the farm = 500+260 = 760
The new number of cows = 300+60 = 260

See how nicely it comes out when the word "percent" is changed to "number".
The new percent of cows is {{{34&2/19}}}%, not 80%!

Answer: 200 sheep originally.

[You might point out this error in wording to your teacher.]

Edwin</pre>