Mr McDonald has some ducks and goats in his farm. If he counted a total of 94 legs and 30 heads, find the number of ducks and the number of goats in his farm.
To find the number of ducks and goats in Mr McDonald's farm, we'll set up a system of equations based on the given information.
Let's assume:
D = number of ducks
G = number of goats
1) The number of legs: Ducks have 2 legs and goats have 4 legs.
Therefore, the equation for the total number of legs can be written as:
2D + 4G = 94
2) The number of heads: Ducks and goats each have one head.
Therefore, the equation for the total number of heads can be written as:
D + G = 30
We now have a system of two equations:
2D + 4G = 94
D + G = 30
To solve this system, there are multiple methods, such as substitution or elimination. Let's solve it by elimination:
Multiply equation 2 by 2 to get:
2(D + G) = 2(30)
2D + 2G = 60
Now we can subtract the modified equation 2 from equation 1 to eliminate D:
(2D + 4G) - (2D + 2G) = 94 - 60
2G = 34
Divide both sides of the equation by 2:
2G/2 = 34/2
G = 17
Substitute the value of G into equation 2 to find D:
D + 17 = 30
D = 30 - 17
D = 13
Therefore, there are 13 ducks and 17 goats in Mr McDonald's farm.
To find the number of ducks and goats, we can set up a system of equations based on the problem's given information.
Let's assume that the number of ducks is represented by 'd' and the number of goats is represented by 'g'.
Each duck has 2 legs, so the total number of duck legs is 2d.
Each goat has 4 legs, so the total number of goat legs is 4g.
According to the problem, the total number of legs is 94. Therefore, we have the equation:
2d + 4g = 94 (Equation 1)
Furthermore, the problem states that there are 30 heads in total. Since each duck and goat has one head, the total number of ducks and goats is 30. Therefore, we have the equation:
d + g = 30 (Equation 2)
Now we have a system of two equations (Equation 1 and Equation 2) with two variables (d and g). We can solve this system to find the values of d and g.
To solve this system, we can use any method like substitution or elimination. Let's use substitution.
From Equation 2, we have:
d = 30 - g
Now substitute this value of "d" in Equation 1:
2(30 - g) + 4g = 94
Simplify and solve for "g":
60 - 2g + 4g = 94
2g = 94 - 60
2g = 34
g = 17
Now substitute this value of "g" into Equation 2 to find "d":
d + 17 = 30
d = 30 - 17
d = 13
Therefore, there are 13 ducks and 17 goats on Mr. McDonald's farm.
number of ducks ---- d
number of goats ----- g
d + g = 30 , they have 1 head each
2d + 4g = 94
or
d + 2g = 47
subtract the two equations:
g = 17
the d + 17 = 30 ----> d = 13
state the conclusion