In a farm ,there are some goats and some chickens. Paul counted 45 heads while Julie counted 150 legs.How many goats and chicken are there?
g = goats
c = chickenes
The 45 heads mean :
Number of goat heads plus the number of chicken heads = 45
g + c = 45
150 legs mean:
4 g (number of goat legs) + 2 c (number of chicken legs) = 150
4 g + 2 c = 150
Now you must solve system of equations:
g + c = 45
4 g + 2 c = 150
Try that.
The solutions are:
c = 15 , g = 30
X goats.
4x Legs.
ns.
45-x Chickens.
2(45-x) = 90 - 2x Legs.
4x + (90-2x) = 150 Legs.
X = 30 Goats.
45-x = 45 - 30 = 15 Chickens.
.
Let's solve this step-by-step:
Step 1: Define the variables.
Let's assume the number of goats as "G" and the number of chickens as "C."
Step 2: Write the given information as equations.
According to the problem, Paul counted 45 heads, which means the total number of goats and chickens is 45. So, we have our first equation:
G + C = 45 (Equation 1)
The problem also states that Julie counted 150 legs. Since goats have 4 legs and chickens have 2 legs, we can write our second equation:
4G + 2C = 150 (Equation 2)
Step 3: Solve the system of equations.
We can solve this system of equations using any method, such as substitution or elimination. Here, I'll use the substitution method.
From Equation 1, we can express G in terms of C:
G = 45 - C
Substituting this value of G into Equation 2, we get:
4(45 - C) + 2C = 150
180 - 4C + 2C = 150
180 - 2C = 150
-2C = 150 - 180
-2C = -30
C = -30 / -2
C = 15
Now, substitute this value of C back into Equation 1 to solve for G:
G + 15 = 45
G = 45 - 15
G = 30
Step 4: Verify the solution.
Now, we have G = 30 and C = 15. Let's check if these values satisfy both equations:
Equation 1: G + C = 45
30 + 15 = 45
45 = 45 (True)
Equation 2: 4G + 2C = 150
4(30) + 2(15) = 150
120 + 30 = 150
150 = 150 (True)
Both equations are true for G = 30 and C = 15.
Step 5: Answer the question.
There are 30 goats and 15 chickens in the farm.
To solve this problem, we can set up a system of equations. Let's assume the number of goats is 'g' and the number of chickens is 'c'.
We know that each goat has one head and four legs, and each chicken has one head and two legs.
From the given information, we can create the following equations:
Equation 1: g + c = 45 (Total number of heads)
Equation 2: 4g + 2c = 150 (Total number of legs)
To solve the system of equations, we can use either substitution or elimination method. Let's use substitution method to solve it:
Solve Equation 1 for 'g':
g = 45 - c
Substitute this value in Equation 2:
4(45 - c) + 2c = 150
180 - 4c + 2c = 150
180 - 150 = 4c - 2c
30 = 2c
c = 15
Substitute c = 15 in Equation 1:
g + 15 = 45
g = 45 - 15
g = 30
Therefore, there are 30 goats and 15 chickens on the farm.