Expert: Ahmed Salami - 10/30/2004

Question
A total of 18 animals are in a field. Some are chickens, some are sheep, and some are cows. The total number of legs is 10 more than 3 times the total number of heads.

Question: how many chickens are in the field?


cal you please help me with this and answer ASAP, thanx.  

Answer
Hi Aisha,
Sorry about the delay. I had a problem with my pc.
Lets say we have x cows, y sheep and z chickens. The number of heads H would be exactly the number of animals i.e
H = x + y + z = 18
Every sheep or cow would have 4 legs while a chicken would only have 2 legs. The number of legs L would be
L = 4x + 4y + 2z
But the question says
L = 3H + 10
4x + 4y + 2z = 3x + 3y + 3z + 10
x + y - z = 10
adding 2z to both sides gives
x + y + z = 2z + 10
but x + y + z = 18
18 = 2z + 10
2z = 8
z = 4
There are thus 4 chickens on the field.
Good luck.
Regards.