Explanation: Let c represent the number of cows in the farmhouse. Let d represent the number of ducks in the farmhouse.
We know that: - there are a total of 61 animals in the farmhouse - one cow has 4 legs - one duck has 2 legs - there are a total of 208 legs
Using the information above, we can create two equations:
c+d=61 4c+2d=208
1) multiply the first equation by 2 If we do this, both equations will have 2d and we can subtract them to solve for c.
c+d=61 2c+2d=122
2) Subtract the first equation from the second
4c+2d=208 2c+2d=122 2c=86 c=43
Therefore, the number of cows in the farmhouse is equal to 43.
2) plug 43 into the first equation to solve for d We can plug 43 into either of the original questions to find the number of ducks, but in this case, it would be easier to solve for in the first equation.
c+d=61 43+d=61 Subtract both sides by 43 43+d-43=61-43 d=18
Therefore, the number of ducks in the farmhouse is equal to 18.
