Question 842204
Farmer Ben owns only cows and ducks. There are a total of 82 animals. One day, for fun, he counts that his animals have a total of 240 legs.

A. Write a single equation with ONE variable to model this situation. Define the variable. 
<pre>
x = the number of cows
80-x = the number of ducks

        number   legs     number
          of      per       of 
       animals  animal     legs
---------------------------------
cows      x        4        4x   
ducks   82-x       2     2(82-x)
---------------------------------
totals   82                240

The equation comes from the right
column:

{{{(matrix(4,1,
Number,of,"cow's",legs))}}}{{{""+""}}}{{{(matrix(4,1,
Number,of,"duck's",legs))}}}{{{""=""}}}{{{(matrix(4,1,
Total,number,of,legs))}}}

4x + 2(82-x) = 240
</pre>
B. Solve the equation to determine how 
many of each animal Farmer Ben owns.
<pre>
 4x + 2(82-x) = 240
4x + 164 - 2x = 240
     2x + 164 = 240
           2x = 76
            x = 38 cows

80-x = the number of ducks = 82-38 = 44 ducks.

Checking: The 38 cows have 38·4 = 152 legs. 
The 44 ducks have 44·2 = 88 legs.

 38+44 = 82 animals
152+88 = 240 legs.

That checks

Edwin</pre>