A farmer keeps hens and rabbits on his farm. One day, he counted a total of 70 heads and 196 legs. How many more hens than rabbits does he have?
You can do it without algebra this way:
All the animals have 1 head and exactly 2 FRONT legs. so 70 animals accounts
for 70*2 or 140 front legs. The remaining 196-140 or 56 hind legs are owned by
the rabbits. Each rabbit has two hind legs, so the 56 hind legs amount to 56÷2
or 28 pairs of hind legs, so there are 28 rabbits and 70-28 or 42 hens, and so
there are 42-28 or 14 more hens that rabbits.
By algebra:
Let h = number of hens
Let r = number of rabbits
Every animal has one head so
number of hens + number of rabbits = number of heads
or
h + r = 70
Hens have exactly 2 legs and rabbits have exactly 4 legs, so
2h + 4r = 196
Solve the system of equations
h + r = 70
2h + 4r = 196
and get h = 42 and r = 28, 42 hens and 28 rabbits.
However the question was not how many of each, but,
>>...How many more hens than rabbits does he have?...<<
So 42 - 28 = 14. So 42 is 14 more than 28, so the answer is 14
more hens than rabbits.
Checking:
Together that's 42+28=70 animals.
The 42 hens have 84 legs and the 28 rabbits have 112 legs.
That's a total of 84+112 = 196 legs.
Edwin