Tulip wrote:

Please could someone help me on the following question.

In a farm there are 13 heads and 40 legs.

a) How many ducks are there ?

b) How many sheep's are there ?

Please explain. Thank you.

I would construct a table of sheep, ducks, heads and legs!

There must be 13 animals as 13 heads.

Where to start well 13 can be split in half as 6 and 7 (no half animals!)

Looks like more sheep than ducks because lots of legs........this is a lucky guess.

7 sheep (4*7=28 legs) 6 ducks (6*2= legs), 13 heads, 40 legs!! Bingo.

I think that was more luck than judgement, expected to try a few variations of ducks and sheep. I expect the question was written so if an 11 year old tried they would get the answer.

For older kids you could use algebra and simultaneous equations.

S + D = 13.................................heads (1)

4S + 2D = 40...............................legs (2)

S=13-D rearaange (1) and substitue into (2)

4(13-D)+2D=40

52-4D+2D=40

52-2D=40

12=2D

D=6

then feed back into (1)

S+6=13

S=7