Q. A small farm has sheep and chickens. There are twice as many chickens as sheep, and there are 104 legs between the sheep and the chickens. How many chickens are there?
c=26
Let's solve this problem step by step:
Step 1: Let's assume the number of sheep as "x".
Step 2: Since there are twice as many chickens as sheep, the number of chickens would be 2x.
Step 3: Each sheep has 4 legs, so the total number of legs contributed by the sheep would be 4x.
Step 4: Each chicken has 2 legs, so the total number of legs contributed by the chickens would be 2 * 2x = 4x.
Step 5: According to the problem, the total number of legs between the sheep and the chickens is 104. So, we can write the equation: 4x + 4x = 104.
Step 6: Combining like terms, we have 8x = 104.
Step 7: Solving for x, divide both sides of the equation by 8: x = 104/8 = 13.
Step 8: Now that we know the value of x, we can substitute it into 2x to find the number of chickens: 2 * 13 = 26.
Therefore, there are 26 chickens on the farm.
To solve this problem, we can set up a system of equations based on the given information.
Let's represent the number of sheep as "S" and the number of chickens as "C".
From the problem, we are told that there are twice as many chickens as sheep, so we can write the equation: C = 2S.
We also know that the total number of legs from the sheep and chickens is 104. Since each chicken has 2 legs and each sheep has 4 legs, we can write another equation: 2C + 4S = 104.
Now we can solve this system of equations to find the number of chickens.
Substituting the value of C from the first equation into the second equation, we get: 2(2S) + 4S = 104.
Simplifying, we have: 4S + 4S = 104.
Combining like terms, we get: 8S = 104.
Dividing both sides by 8, we find: S = 13.
Now that we know the number of sheep is 13, we can substitute this value back into the equation C = 2S to find the number of chickens:
C = 2 * 13
C = 26.
Therefore, there are 26 chickens on the farm.
c = 2s
2c+4s=104
now solve for c