How many chickens and goats are there if those animals have 26heads and 68legs?
Question by Lovely: How many chickens and goats are there if those animals have 26heads and 68legs?
Tricia’s grandfather has chickens and goats on his farm.She asked him how many chickens and goats he has.Her grandfather told her that his animals had 26 heads and 68 legs. How many chickens and goats are there in the farm?
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2 Responses to How many chickens and goats are there if those animals have 26heads and 68legs?
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Assuming that all of the animals have all their limbs, i.e. goats have 4 legs and 1 head, chickens have 2 legs and 1 head:
Using simultaneous equations, where x represents chickens and y, goats;
(1) 2x + 4y = 68 (legs)
(2) x + y = 26 (heads)
Multiply (2) by 2 to get:
(1) 2x + 4y = 68 (legs)
(3) 2x + 2y = 52 (heads)
Subtract (3) from (1) to get:
(4) 2y = 16
Therefore:
(5) y = 8
Use 8 instead of y in (2):
(6) x + 8 = 26
Therefore:
(7) x = 26 – 8 = 18
So:
y = 8 —> 8 goats
x = 18 —> 18 chickens
James
February 5, 2014 at 4:33 am
26 heads -> 26 animals
If all the animals were chickens, there would be 26 x 2 = 52
But there are 68 legs,
68 – 52 = 16
If there are 16 extra legs and the difference between the number of legs chickens and goats had were 2, there are,
16/2 = 8
There are 8 goats and 18 chickens
VanillaGirl
February 5, 2014 at 4:54 am