Pigs and Chickens

Solving the Problem of the Pigs and Chickens

The Problem: The farmer keeps only two kinds of animals: pigs and chickens. There are 18 animal heads and 50 animal legs. How many chickens does the farmer have? How many pigs does the farmer have?

What is the main problem?  Too many students look for the numbers in the problem and try to decide if they should add, subtract, multiply or divide. If you divide 50 legs by 18 heads you’d get 2.77… which doesn’t make any sense.

First you must realize there are two questions. You need two answers. Then, there is an important piece of information missing. Pigs have four legs. Chickens have two legs.

Method 1: Guess and check. Students often try this method first. They know that with 18 heads there are 18 animals. There might be 9 chickens and 9 pigs. They check to see if this works:  9 chickens x 2 legs = 18 legs.  9 pigs x 4 legs = 36 legs.  18+36= 54 legs. Some students think about this and can see if there should be more chickens or more pigs. I’d call that intelligent guess and check. Simple drawing of pig and chicken

Method 2: Draw a picture.
Younger children can solve this problem by drawing pictures of pigs and chickens.   After drawing a group of pigs and a group of chickens, they cross out some pictures and add others until they reach the answer.

Method 3: Using a Chart.  You might start by listing all the possibilities:  The top of the chart would read:
Pigs       Pig Legs    Chickens   Chicken Legs    Total Legs
0                  0                   18                   36                        36
1                 4                   17                    34                       38

You could finish the chart – or at least enough of it – and find the answer.

Method 3: Using Algebra. But this isn’t as simple as you might expect.
Let P  =  number of pigs
Let C =  number of chickens
P  +  C = 18
4P + 2C = 50
I asked this or a similar question in a high school physics class.  If those students had been in a math class, they’d have used algebra. But, for some reason, in a science class, most of them started with guess and check or a chart.

It is helpful to see that there are different options. If you couldn’t figure out how to state the problem algebraically or if you didn’t remember how to solve the problem this way, would you give up or try  guess and check to get your answer?