Question 477893
<p>Set C as the total number of cows. Set G as the grazing cows, S as the sleeping cows, and D as the drinking cows.  Set up the equation like so;
</p>

Total numbers of cows=all grazing, sleeping, and drinking cows.
{{{C=G+S+D}}}

Half the total cows are grazing:
{{{G=(1/2)C}}}

Three fourths of the REMAINING cows are sleeping
{{{S=(3/4)(C-G)}}}

9 cows are drinking from the pond
{{{D=9}}}


Plug all these answers into the original equation {{{C=G+S+D}}} and get {{{C=(1/2)C+(3/4)(C-(1/2)C)+9}}}


Now simplify:

{{{C=(1/2)C+(3/8)C+9}}}

Combine all the C's on both sides:

{{{(1/8)C=9}}}

Now multiply both sides by 8:

{{{C=72}}}

Answer: 72 cows

To check, plug in 72 for C.

There are 72 cows, if half of them are grazing, then 36 are grazing. If three-fourths of the rest (36 more) are sleeping, then 27 are sleeping, which leaves 9 drinking.