the total number of cows and ducks on a farm is 35.All the cows have 74 more legs than all the ducks.How many cows are there on the farm?
D = Number of Ducks
C = Number of Cows
D + C = 35
C = 35 - D
Duck have 2 legs.
Cow have 4 legs
All the cows have 74 more legs than all the ducks.
This mean :
4 * C = 2 D + 74
4 * ( 35 - D ) = 2 D + 74
4 * 35 - 4 D = 2 D + 74
140 - 4 D = 2 D + 74 Subtract 74 to both sides
140 - 4 D - 74 = 2 D + 74 - 74
66 - 4 D = 2 D Add 4 D to both sides
66 - 4 D + 4 D = 2 D + 4 D
66 = 6 D Divide both sides by 6
66 / 6 = 6 D / 6
11 = D
D = 11
C = 35 - 11 = 24
Solution 24 Cows and 11 Ducks
Proof :
24 Cows have :
4 * 24 = 96 legs
11 Duck have :
11 * 2 = 22 legs
96 - 22 = 74
To solve this problem, we need to set up a system of equations based on the information given.
Let's assume the number of cows on the farm is "c" and the number of ducks is "d".
From the problem statement, we know that the total number of animals is 35:
c + d = 35 ---(Equation 1)
We also know that all the cows have 74 more legs than all the ducks. Since a cow has four legs and a duck has two legs, we can calculate the total number of legs for the cows and ducks:
4c (total number of cow legs) = 2d (total number of duck legs) + 74
Simplifying this equation, we get:
4c = 2d + 74 ---(Equation 2)
Now we can solve this system of equations.
We'll start by rearranging Equation 1 to express "d" in terms of "c":
d = 35 - c
Substituting this into Equation 2:
4c = 2(35 - c) + 74
4c = 70 - 2c + 74
6c = 144
c = 24
Therefore, there are 24 cows on the farm.