Question 1132356
.


            Actually,  it is an entertainment problem,  and a good style and a tradition requires it to be solved by a special method.



<U>One line solution</U>


<pre>
The number of cows = {{{(64-20*2)/(4-2)}}} = {{{24/2}}} = 12.         <U>ANSWER</U>:  12 cows.

The rest  20 - 12 = 8  are  chickens.            <U>ANSWER</U>:   8 chickens.


<U>Check</U>.  8*2 + 12*4 = 64 legs.   ! Correct !
</pre>



<U>Explanation to the one line solution</U>


<pre>
    There is no need to explain that each chicken has 2 legs, while each cow has 4 legs.


    Let assume for a minute that all creatures in this problem have 2 legs each.


    Then the total number of legs would be 2*20 = 40.


    But we are given 64 legs.


    The shortage  of  64-40 = 24 legs occurred because we assumed and counted only 2 legs for each cow, same as for each chicken.


    So we need to fix our calculations, by returning 2 legs with each cow.


    Therefore, we divide  64-40 = 24 legs  by  2 = (4-2), exactly as the "one line formula" does it, and obtain 
    our answer - the number of cows - in this way.
</pre>

Solved.


-------------------


It is totally legal solution. &nbsp;&nbsp;&nbsp;&nbsp; // &nbsp;&nbsp;&nbsp;&nbsp; I mean - it is not a joke !


See the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/misc/Problem-on-two-wheels-and-three-wheels-bicycles-in-a-sale.lesson>Problem on two-wheel and three-wheel bicycles</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/misc/Problem-on-animals-at-a-farm.lesson>Problem on animals at a farm</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/misc/Problem-on-tablets-in-containers.lesson>Problem on pills in containers</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/misc/What-type-of-problems-are-these.lesson>What type of problems are these?</A> 

in this site and find there many other similar problems solved by the same method.


This method is applicable to traditional coin problems; &nbsp;to standard ticket problems; &nbsp;and even to traditional and standard 
mixture problems.


It works in this problem and in all mentioned problems in an equal basis with the true &nbsp;Algebra methods, &nbsp;such as 
reducing to a single linear equation or reducing to systems of linear equations.


Moreover, &nbsp;when you will learn Algebra more, &nbsp;you will understand and will recognize that this &nbsp;"one line formula" &nbsp;is nothing else 

as the solution by the determinant method, &nbsp;which is the same as the Cramer's rule.


So, &nbsp;this "one line formula" is simply a shortcut for these more complicated methods.


Armed with the logic of this solution, &nbsp;you will be able to solve many similar problems even without using equations
(practically MENTALLY) &nbsp;with this shortcut formula, &nbsp;and the logic will lead you and will prevent you of making errors, 
when you use this "one line formula" method.



In this way, &nbsp;through the given entertainment problem you get better understanding Algebra, &nbsp;as well as the fast solution method 
in your hands.



It is why I wrote this post.