Farmer Greg has some cows and some hens. Between them they have 52 legs and 38 eyes. How many hens, and how many cows does farmer Greg have?
Clue..
Cows have four legs
Hens have 2 legs
Eyes 2
What I got..
38÷2=19
8×4=32
10×2=20
20+32=52
The legs add up, but the eyes do not. You are correct that there are 19 animals. But then you go on to finish wrong.
If there are m cows (moo) and c hens (cluck),
4m+2c = 52
2m+2c = 38
2m = 14
m = 7
7 cows and 12 chickens
7*4+12*2 = 28+24 = 52 legs
2*(7+12) = 2*19 = 38 eyes
Let's solve this step-by-step:
1. We know that the total number of legs is 52.
- Cows have 4 legs each.
- Hens have 2 legs each.
Let's assume there are x cows and y hens. Therefore, the total number of legs can be expressed as:
4x + 2y = 52
2. We also know that the total number of eyes is 38, and since each animal has 2 eyes:
2(x + y) = 38
Now, let's solve these equations to find the values of x (number of cows) and y (number of hens):
From equation 2, we can simplify it as:
2x + 2y = 38
x + y = 19 (Divide both sides by 2)
We can rewrite this equation as:
x = 19 - y
Now we substitute this value of x back into equation 1:
4(19 - y) + 2y = 52 (Replace x with 19 - y)
Simplifying this equation:
76 - 4y + 2y = 52
-2y = 52 - 76
-2y = -24
y = -24 / -2
y = 12
Now that we have the value of y (number of hens), we can substitute it back into equation 2 to find x:
x + 12 = 19
x = 19 - 12
x = 7
Therefore, Farmer Greg has 7 cows and 12 hens.
To solve this problem, we can use a system of equations. Let's assume the number of cows is represented by 'x', and the number of hens is represented by 'y'.
According to the information given, we know that cows have four legs and hens have two legs. Therefore, the total number of legs can be represented by the equation:
4x + 2y = 52
Similarly, the total number of eyes can be represented as 2x + 2y = 38, since both cows and hens have two eyes each.
Now, we have a system of equations:
4x + 2y = 52
2x + 2y = 38
We can solve this system of equations either by substitution or elimination.
Using elimination, we can subtract the second equation from the first equation:
(4x + 2y) - (2x + 2y) = 52 - 38
2x = 14
x = 7
Now, substitute the value of x into one of the equations:
2(7) + 2y = 38
14 + 2y = 38
2y = 24
y = 12
Therefore, Farmer Greg has 7 cows and 12 hens.