A farmer raises chickens and goats. She knows she has 22 animals all together. All together her animal has 56 feet. how many of each type of animal does she have?
You didn't describe further how will get c=16
G=6
And more is 16+6=22
So 32+24=56
Let's solve this problem step-by-step.
Step 1: Determine the number of chickens.
Let's assume the number of chickens is "c".
Step 2: Determine the number of goats.
Since there are a total of 22 animals and we already know the number of chickens is "c", we can determine the number of goats by subtracting the number of chickens from the total number of animals:
Number of Goats = Total number of animals - Number of Chickens
Number of Goats = 22 - c
Step 3: Calculate the number of feet for chickens.
Chickens have 2 feet each. So, the total number of feet for chickens is:
Number of Chicken Feet = Number of Chickens * 2
Number of Chicken Feet = 2c
Step 4: Calculate the number of feet for goats.
Goats have 4 feet each. So, the total number of feet for goats is:
Number of Goat Feet = Number of Goats * 4
Number of Goat Feet = (22 - c) * 4
Step 5: Set up an equation for the total number of feet.
According to the problem, the total number of feet is 56. So, we'll set up the equation:
Total Number of Feet = Number of Chicken Feet + Number of Goat Feet
56 = 2c + (22 - c) * 4
Step 6: Solve the equation.
Simplify the equation:
56 = 2c + 88 - 4c
Combine like terms:
56 - 88 = -2c
-32 = -2c
Divide both sides by -2:
16 = c
Step 7: Calculate the number of goats.
Now that we know the number of chickens (16), we can substitute it into the equation from Step 2 to find the number of goats:
Number of Goats = 22 - c
Number of Goats = 22 - 16
Number of Goats = 6
Step 8: Check the solution.
We have found that there are 16 chickens and 6 goats. We can validate this by checking if the total number of feet adds up to 56:
Number of Chicken Feet = Number of Chickens * 2 = 16 * 2 = 32
Number of Goat Feet = Number of Goats * 4 = 6 * 4 = 24
Total Number of Feet = 32 + 24 = 56
The total number of feet matches the given information, so our solution is correct.
Therefore, the farmer has 16 chickens and 6 goats.
To solve this problem, we can set up a system of equations based on the given information. Let's use the variables "c" to represent the number of chickens and "g" to represent the number of goats.
1) The total number of animals is 22:
c + g = 22
2) The total number of feet is 56:
2c + 4g = 56
We use 2c and 4g because each chicken has 2 feet and each goat has 4 feet.
Now, we can solve these equations to find the values of c and g.
From equation (1), we can rearrange it to express c in terms of g:
c = 22 - g
Substitute this value of c in equation (2):
2(22 - g) + 4g = 56
Simplify the equation:
44 - 2g + 4g = 56
2g = 56 - 44
2g = 12
g = 12 / 2
g = 6
Now, substitute the value of g back into equation (1) to find c:
c + 6 = 22
c = 22 - 6
c = 16
So, the farmer has 16 chickens and 6 goats.
Okay, the chickens have 2 feet and the goats have 4. So let’s make the number of chicks C and the number of goats G.
So the number of legs would be 2 x C + 4 x G which is equal to the total number of feet, or 56
2C + 4G = 56
And, we know she has 22 altogether, right? So C + G = 22
Now, you have 2 equations and can solve.
C=22-G
2C + 4G = 56
Or 2 [22-G] + 4G = 56
44-2G+4G=56
44+2G=56
2G=12
G=6
So, the number of goats is 6, and that means the number of chicks has to be 16.
See?