There are 1000 rabbits and chickens on a farm, and together they have 3150 legs. How many rabbits and how many chickens are there on the farm?
number of rabbits ---- r
number of chickens = 1000 - r
rabbits have 4 legs, and chickens have 2 legs, so
4r + 2(1000 - r) = 3150
solve for r, and you have the number of rabbits,
chicken number is 1000 - the r value you found
To find the number of rabbits and chickens on the farm, we can set up a system of equations based on the information given.
Let's assume the number of rabbits is represented by 'R' and the number of chickens is represented by 'C'.
R + C = 1000 (Equation 1)
Since rabbits have 4 legs and chickens have 2 legs, we can express the total number of legs using these equations:
4R + 2C = 3150 (Equation 2)
Now, we can solve this system of equations to find the values of R and C.
To solve the system of equations, we can use the substitution method or elimination method.
Let's use the substitution method:
From Equation 1, we can express C in terms of R:
C = 1000 - R
Substituting this expression for C into Equation 2, we get:
4R + 2(1000 - R) = 3150
Simplifying the equation:
4R + 2000 - 2R = 3150
2R = 3150 - 2000
2R = 1150
R = 575
Now that we have found the number of rabbits (R = 575), we can substitute this value into Equation 1 to find the number of chickens:
575 + C = 1000
C = 1000 - 575
C = 425
Therefore, there are 575 rabbits and 425 chickens on the farm.