Question

A farmer raises cows and chickens. The farmer has a total of 25 animals. One day he counts the legs of all of his animals and counts a total of 64 legs.

Let x = number of cows.
Let y = number of chickens.

Which system of equations can be used to solve for the number of cows and the number of chickens on the farm?

Answer 1

The system of equations to determine the number of cows and chickens is x + y = 25 and 4x + 2y = 64, where x is the number of cows and y is the number of chickens.

Step-by-step explanation:

To find the number of cows and chickens on the farm, we can set up a system of linear equations using the given variables x for the number of cows and y for the number of chickens. Since we know the total number of animals is 25, one equation would represent this total: x + y = 25. Additionally, since cows have 4 legs and chickens have 2 legs, and the farmer counted a total of 64 legs, another equation would represent the total number of legs: 4x + 2y = 64.

Therefore, the system of equations to solve for the number of cows and chickens is:

• x + y = 25
• 4x + 2y = 64

Answer 2

Step-by-step explanation:

x + y = 25 ...........................(1)

{4x + 2y =64} / 2 divide the equation by 2

2x + y = 32 ........................(3)

Step Two

subtract (1) from (3)

2x + y = 32

x + y = 25

x = 7

Therefore from equation 1 we get x + y = 25

but x = 7

7 + y = 25 Subtract 7 from both sides.

y = 25 - 7

y = 18

Check

4*x + 2*y = 64

4*7 + 2*18 =? 64

28 + 36 = ? 64

64 = 64

The checks out to be the right answer.