A farmer counted the number of cows and chickens by counting heads and legs. If he counted 35 heads and 78 legs, how many cows and how many chickens did he have?
If there are x cows and y chickens, you know (counting heads)
x+y = 35
Now, counting legs, you know:
???
Work that out, then solve the two equations.
lukik65j
To solve this problem, we can use a system of equations. Let's represent the number of cows as "c" and the number of chickens as "h".
We have two pieces of information:
1. The total number of heads is 35: c + h = 35
2. The total number of legs is 78: 4c + 2h = 78 (since cows have 4 legs and chickens have 2 legs)
Now, we can solve these equations simultaneously to find the values of c and h.
First, we can use substitution to eliminate one variable. Rearranging the first equation, we can express c in terms of h: c = 35 - h.
Substituting this expression for c in the second equation:
4(35 - h) + 2h = 78
140 - 4h + 2h = 78
-2h = -62
h = 31
So, there are 31 chickens.
Plugging this value back into the first equation:
c + 31 = 35
c = 35 - 31
c = 4
Thus, the farmer has 4 cows and 31 chickens.