Old macdonald looked out his window and saw some cows and chickens. there were a total of 28 animals and 74 legs. assuming that all the cows have 4 legs , and all the chickens have 2 legs, how many of each animal did old mcdonald see

For word problems, assign variables so you can express them into equations. For this problem, the unknown is the number of each animals. Let's assign x to the number of cows and y to the number of chickens. It is mentioned that there are a total of 28 animals. Therefore, we can formulate the first independent equation to be

x + y = 28  ---> eqn 1

Next, we know that the total number of legs are 74. Since each cow has 4 legs and each chicken has 2 legs, the second independent equation we could formulate is:

4x + 2y = 74 ---> eqn 2

Now, we have a system of linear equations. There are two unknowns and two independent equations. Thus, the system is solvable. Let's use the method of substituting to solve this. Rearrange eqn 1 such that x is a function of y. Let's denote this as eqn 1'.

x = 28 - y ---> eqn 1'

Substitute eqn 1' to eqn 2:

4(28 - y) + 2y = 74
112 - 4y + 2y = 74
-2y = 74 - 112
-2y = -38
y = -38/-2
y = 19

Therefore, there are 19 chickens. Now, we use y=19 to substitute to eqn 1:

x + 19 = 28
x = 28 - 19
x = 9

Therefore, there are 9 cows.