number of chickens --- c
number of pigs ---- p
c+p = 220
2c + 4p = 520 or c + 2p = 260
subtract then
p = 40
back into the first
c+40 = 220
c = 180
180 chickens, 40 pigs
using systems of equations to solve
number of pigs ---- p
c+p = 220
2c + 4p = 520 or c + 2p = 260
subtract then
p = 40
back into the first
c+40 = 220
c = 180
180 chickens, 40 pigs
We know that the total number of animals on the farm is 220, so we can write the equation:
c + p = 220 -- Equation 1
We also know that the total number of legs on the farm is 520. Since chickens have 2 legs and pigs have 4 legs, we can write the equation:
2c + 4p = 520 -- Equation 2
To solve the system of equations, we can use the method of substitution or elimination. I'll use the method of substitution.
From Equation 1, we can express c in terms of p:
c = 220 - p
Now substitute this value of c into Equation 2:
2(220 - p) + 4p = 520
440 - 2p + 4p = 520
2p = 520 - 440
2p = 80
p = 80/2
p = 40
Now substitute this value of p back into Equation 1 to find the number of chickens:
c + 40 = 220
c = 220 - 40
c = 180
Therefore, there are 180 chickens and 40 pigs on the farm.
We can set up two equations based on the given information:
Equation 1: x + y = 220 (Total number of chickens and pigs)
Equation 2: 2x + 4y = 520 (Total number of legs)
Now, we have a system of equations. To solve for the values of 'x' and 'y', we can use one of the methods such as substitution or elimination.
Method 1: Substitution
From Equation 1, we can express x in terms of y: x = 220 - y
Substituting this value of x into Equation 2:
2(220 - y) + 4y = 520
440 - 2y + 4y = 520
2y = 520 - 440
2y = 80
y = 40
Now, substituting the value of y back into Equation 1 to solve for x:
x + 40 = 220
x = 220 - 40
x = 180
Therefore, there are 180 chickens and 40 pigs on the farm.