Answer:
There are 51 chickens and 49 goats in the barnyard.
To find the number of chickens and goats, let's denote the number of chickens as C and the number of goats as G. Each chicken has 2 feet, and each goat has 4 feet.
So, the total number of feet can be calculated by multiplying the number of chickens by 2 and the number of goats by 4, and then summing these two values.
We can express this mathematically as:
2C + 4G = 298
Now, we also know that the total animals is 100:
C + G = 100
Now, we have a system of two equations:
2C + 4G = 298
C + G = 100
We can solve this system for C and G:
C + G = 100
C = 100 - G
Substitute this expression for C into the first equation:
2(100 - G) + 4G = 298
Now solve for G:
200 - 2G + 4G = 298
2G = 98
G = 49
Now that we have G, we can substitute back into the second equation to find C:
C = 100 - 49
C = 51
Therefore, there are 51 chickens and 49 goats in the backyard.
