When Josh was visiting his family’s farm, he saw that the farm only raised chickens and cows. Josh counted 38 heads and 100 feet in the barnyard. How many chickens and how many cows were in the barnyard?: *
26 chickens and 12 cows
20 chickens and 18 cows
23 chickens and 15 cows
29 chickens and 9 cows
The first combination would have 38 heads and 74 feet, so that doesn't fit.
Try the others yourself and see which combination works
26 chickens and 12 cows
To solve this problem, we can use a system of equations. Let's assign variables to represent the number of chickens and cows in the barnyard.
Let's say x represents the number of chickens and y represents the number of cows.
According to the problem, we know that the total number of heads is 38:
x + y = 38 ...(equation 1)
We also know that the total number of feet in the barnyard is 100:
2x + 4y = 100 ...(equation 2)
Let's solve this system of equations to find the values of x and y, which represent the number of chickens and cows, respectively.
Multiplying equation 1 by 2, we get:
2x + 2y = 76 ...(equation 3)
Subtracting equation 3 from equation 2, we get:
(2x + 4y) - (2x + 2y) = 100 - 76
2y = 24
y = 12
Now, substituting the value of y=12 into equation 1, we get:
x + 12 = 38
x = 26
Therefore, there are 26 chickens and 12 cows in the barnyard.
So the correct answer is 26 chickens and 12 cows.