A farmer has ducks and cows they have 22 heads and 56 legs how much of each animal? I really don't get this :/
d has 2 legs
c has 4 legs
each has one head
so
d + c = 22
2d + 4c = 56 or d + 2c = 28
d + c = 22
d + 2c = 28
------------ subtract
0 - c = -6
c = 6
then d = 22-6 = 16
To solve this problem, we need to set up a system of equations using the information given.
Let's assume that the number of ducks is represented by 'd' and the number of cows is represented by 'c'.
According to the problem, the total number of heads is 22. Since each animal has one head, we can express this as:
d + c = 22 -- Equation 1
Now let's consider the total number of legs. Ducks have two legs, while cows have four legs. Hence, the total number of legs can be expressed as:
2d + 4c = 56 -- Equation 2
Now you have a system of equations with two variables (d and c), so you can solve them simultaneously.
There are several methods to solve this system, but let's use the substitution method.
From Equation 1, we can solve for d:
d = 22 - c -- Equation 3
Now we substitute Equation 3 into Equation 2:
2(22 - c) + 4c = 56
44 - 2c + 4c = 56
2c = 12
c = 6
Now that we have the value of 'c', we can substitute it back into Equation 1 to find 'd':
d + 6 = 22
d = 22 - 6
d = 16
Therefore, there are 16 ducks and 6 cows on the farm to satisfy the conditions of having 22 heads and 56 legs.
I hope this explanation helps you understand how to solve this problem!