Count ostriches and llamas. Someone counted 47 heads and 122 legs. How many of each animals is on the farm.
a = number of ostriches
b = number of llamas
Numbers of heads = 47
That mean numbers of animals = 47
Numbers of animals = number of ostriches + number of llamas
a + b = 47
Numbers of legs = 122
Ostriches have two legs and llamas have four legs so :
2a + 4 b = 122
Now you must solve system of two equations :
a + b = 47
2a + 4 b = 122
The solutions are :
a = 33
b = 14
There are 33 ostriches and 14 llamas.
33 ostriches and 14 llamas
Let's denote the number of ostriches as "o" and the number of llamas as "l".
From the given information, we can determine two conditions:
1. The total number of heads: o + l = 47
2. The total number of legs: 2o + 4l = 122
To solve this system of equations, we can use the method of substitution.
Let's solve equation 1 for o:
o = 47 - l
Substituting this value of o into equation 2:
2(47 - l) + 4l = 122
94 - 2l + 4l = 122
2l = 28
l = 14
Substituting this value of l back into equation 1:
o = 47 - 14
o = 33
Therefore, there are 33 ostriches and 14 llamas on the farm.
To solve this problem, we can set up a system of equations based on the given information. Let's assign variables to represent the number of ostriches and llamas on the farm.
Let's say "o" represents the number of ostriches, and "l" represents the number of llamas.
Since ostriches have one head and two legs, and llamas have one head and four legs, we can write two equations:
Equation 1: o + l = 47 (the total number of heads)
Equation 2: 2o + 4l = 122 (the total number of legs)
Now we can solve the system of equations to find the values of "o" and "l".
We can use substitution or elimination methods to solve the system. Let's use the substitution method in this case.
From Equation 1, we can isolate "o":
o = 47 - l
Substitute this value into Equation 2:
2(47 - l) + 4l = 122
Now, let's simplify the equation:
94 - 2l + 4l = 122
Combine like terms:
2l = 122 - 94
2l = 28
Divide by 2:
l = 14
Now, substitute this value of "l" back into Equation 1 to find the value of "o":
o + 14 = 47
o = 47 - 14
o = 33
Therefore, there are 33 ostriches and 14 llamas on the farm.