Question

In a poultry farm having hens and pigs, Mawia can see 84 heads and 282 legs. How many hens are there on the farm?

A. 18
B. 21
C. 24
D. 27

Answer 1

Using a system of equations based on the number of heads and legs, we determine that the farm has 27 hens, represented by option D.

Step-by-step explanation:

The question asks us to determine the number of hens on a farm when there are a total of 84 heads and 282 legs visible. We can set up a system of equations to solve this problem since hens have 2 legs and pigs have 4 legs. If we let H represent hens and P represent pigs, we can write two equations based on the heads and legs:

1. H + P = 84 (each animal has one head)
2. 2H + 4P = 282 (each hen has 2 legs and each pig has 4 legs)

To solve for the number of hens, we can multiply the first equation by 2 and subtract it from the second equation to eliminate P from the equations:

2H + 2P = 168 (multiplying the first equation by 2)

Now subtract this from the second equation:

2H + 4P - (2H + 2P) = 282 - 168

2P = 114

P = 57

Now that we know there are 57 pigs, we can substitute back into the first equation to find the number of hens (H):

H = 84 - P

H = 84 - 57

H = 27

Therefore, there are 27 hens on the farm, which corresponds to option D.