Question

2) A farmhouse shelters 61 animals. Some are cows and some are ducks. Altogether there are

Answer 1

Answer:
43 cows and 18 ducks

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.

I hope this helps!