Trial and Improvement

Prompt poster: PDF Printable version: PDF Word

On the Farm

In the farmyard there are some pigs and some chickens. There are 87 animals and 260 legs. How many pigs are there in the farmyard?

When children first meet this type of problem they are often floored.

The strategy to get them started is probably guess and check.

For example:

I guess there are 50 pigs so there are 37 chickens to make 87 animals. A pig has 4 legs and a chicken has 2 legs.

50 x 4 = 200
37 x 2 = 74   (using multiplication skills)
200 + 74 = 274   too high

Now employ a new strategy: Guess and improve.

Pigs have four legs so I need fewer pigs and more chickens. I'll guess 40 pigs so there will be 47 chickens.

40 x 4 = 160
47 x 2 = 94
160 + 94 = 254   too small

OK so now I know that there are between 40 and 50 pigs. I'll try 45 pigs so there are 42 chickens.

45 x 4 = 180
42 x 2 = 84
180 + 84 = 264   too high - but only just!

So I'll try one less pig. 44 pigs and 43 chickens.

44 x 4 = 176
43 x 2 = 86
176 + 86 = 262   nearly there

Getting rid of one pig reduced the number of legs by 2... so one fewer pigs will give 260 legs (recognising patterns)

So 43 pigs and 44 chickens.

43 x 4 = 172
44 x 2 = 88
172 + 86 = 260

There are 43 pigs and 44 chickens.

So with this type of problem the answers can oscillate backwards and forwards until a solution is reached.