Answer: 15 chickens and 30 rabbits on the farm
Explanation:
To solve this problem, let's use a system of equations. Let's say "g" represents the number of chickens and "c" represents the number of rabbits.
From the given information, we know that the total number of heads (chickens and rabbits) is 45 and the total number of legs (chickens have 2 legs and rabbits have 4 legs) is 150.
1. Start by setting up two equations based on the given information:
g + c = 45 (equation 1) - This equation represents the total number of heads.
2g + 4c = 150 (equation 2) - This equation represents the total number of legs.
2. Solve equation 1 for g:
g = 45 - c
3. Substitute g in equation 2 with 45 - c:
2(45 - c) + 4c = 150
4. Simplify and solve for c:
90 - 2c + 4c = 150
2c = 60
c = 30
5. Substitute the value of c back into equation 1 to find g:
g + 30 = 45
g = 15
Therefore, there are 15 chickens and 30 rabbits on the farm.