Question

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

Answer 1

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.