Chickens and rabbits

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

Correct answer:

a =  10
b =  20

Step-by-step explanation:

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

7 years ago  50 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.

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

3 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

3 years ago  2 Likes




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