Chickens and rabbits

In a farmyard there were chickens and rabbits. Together they had 30 heads and 100 legs. How many chickens and how many rabbits were in the yard?

Final Answer:

a =  10
b =  20

Step-by-step explanation:

a+b=30 2⋅ a+4⋅ b=100  2a+4b=100  Pivot:Row1↔Row2  Row2−21​⋅ Row1→Row2 −b=−20  b=−1−20​=20 a=2100−4b​=2100−4⋅ 20​=10  a=10 b=20

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Showing 4 comments:
Math student
We know that chicken has 2 legs and rabbit has 4. Assume that all heads are of chicken = 44*2 = 88. Now the difference between the total no. Of legs = 124-88 = 36. 36/2 =18 legs of Rabbits and 44-18 = 26 for chicken

8 years ago  51 Likes
Math student
40 chickens means 80 legs rest 10 legs .rabbit has 4 legs or 2 legs?10 legs will be shared among rabbit.

6 years ago  6 Likes
Qing.
Can you give a better explanation? I can't understand it tho.

4 years ago  4 Likes
Human
Q: what about if there was 56 heads and 170 legs?
A:  There are:
a = 27 chicken
b = 29 rabbit

see calculation: https://www.hackmath.net/en/calculator/solving-system-of-linear-equations?input=a%2Bb+%3D+56%0D%0A2*a%2B4*b%3D170&submit=Calculate

4 years ago  2 Likes




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