Question 1126410: simon saw antelopes and crows in the meadow at the zoo. He counted 26 heads and 66 legs. How many antelopes did he see?
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52776)   (Show Source):
You can put this solution on YOUR website! .
Actually, it is an entertainment problem, and a good style and a tradition requires it to be solved by a special method.
One line solution
The number of antelopes =  = 7. ANSWER: 7 antelopes.
Check. 7*4 + (26-7)*2 = 66 legs. ! Correct !
Explanation to the one line solution
There is no need to explain that each crow has 2 legs, while each antelope 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*26 = 52.
But we are given 66 legs.
The shortage of 66-52 = 14 legs is because we assumed and counted only 2 legs for each antelope, same as for each crow.
So we need to fix our calculations, by returning 2 legs with each antelope.
Therefore, we divide 66-52 = 14 legs by 2 = (4-2), exactly as the formula does, and obtain
our answer - the number of antelopes - in this way.
Solved.
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It is totally legal solution. // I mean - it is not a joke !
See the lessons
- Problem on two-wheel and three-wheel bicycles
- Problem on animals at a farm
- Problem on pills in containers
- What type of problems are these?
in this site and find there many other similar problems solved by the same method.
This method is applicable to traditional coin problems; to standard ticket problems; 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 Algebra methods, such as
reducing to a single linear equation or reducing to systems of linear equations.
Moreover, when you will learn Algebra more, you will understand and will recognize that this "one line formula" is nothing else
as the solution by the determinant method, which is the same as the Cramer's rule.
So, this "one line formula" is simply a shortcut for these more complicated methods.
Armed with the logic of this solution, you will be able to solve many similar problems even without using equations
(practically MENTALLY) with this shortcut formula, and the logic will lead you and will prevent you of making errors,
when you use this "one line formula" method.
In this way, through the given entertainment problem you get better understanding Algebra, as well as the fast solution method in your hands.
It is why I wrote this post.
Answer by MathTherapy(10551)  (Show Source):
You can put this solution on YOUR website!
simon saw antelopes and crows in the meadow at the zoo. He counted 26 heads and 66 legs. How many antelopes did he see?
Let number of antelopes and crows be A, and C, respectively
Then we get: A + C = 26 ------- eq (i)
Also, 4A + 2C = 66______2(2A + C) = 2(33)______2A + C = 33 ------ eq (ii)
Subtracting eq (i) from eq (ii), we get: A, or number of antelopes = 
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