Old McDonald has cows and chickens on his farm. If the animals on his farm have a total of 197 heads and 634 legs, how many cows does Old McDonald have?
Note: A cow has 1 head and 4 legs. A chicken has 1 head and 2 legs.
To find out how many cows Old McDonald has, we need to set up a system of equations based on the total number of heads and legs.
Let's define:
C = Number of cows
H = Number of chicken
Total Heads: C + H = 197
Total Legs: 4C + 2H = 634
Now, let's solve this system of equations to find the value of C (number of cows):
From the first equation, we can rearrange it to get H = 197 - C.
Substituting this value of H in the second equation:
4C + 2(197 - C) = 634
4C + 394 - 2C = 634
2C + 394 = 634
2C = 634 - 394
2C = 240
C = 240/2
C = 120
Therefore, Old McDonald has 120 cows on his farm.
number of cows = x
number of chickens = y
x+y = 197
4x + 2y = 634 or 2x + y = 317
subtract 2nd - 1st:
x = 120
back into the first:
120+y = 197
y = 77
120 cows and 77 chickens