3. Farmer John has cows and chickens on his farm. His farm animals have 128 legs and 48 heads total. How many cows and how many chickens are on the farm? a. Explain what 128 represents, and how it relates to the cows and chickens. b. Explain what 48 represents, and how it relates to the cows and chickens. Setup a system, of two equations, to help you solve this riddle. d. Solve this system using either Elimination or Substitution, show your work, and state your answer as a complete sentence. C.
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First, each cow and chicken has one head each, obviously. That means that the 48 corresponds to the total number of animals on Farmer John's farm. Since chickens have 2 legs and cows have 4 legs, that means that the 128 represents the separate amount of cows and chickens there are. We can let c equal the number of cows, and h equal the number of chickens. We know that the total number of animals is 48, so c + h = 48. We know that for each cow, there are 4 legs, and for each chicken there are 2 legs, so 4c + 2h = 128.

Now, we can solve by substitution. Multiplying the first equation by 2, we have 2c + 2h = 96. We can subtract this from the second equation to get 2c = 32, and c = 16. That means there are 16 cows on the farm, and since c + h = 48, there are 48 - 16 = 32 chickens on the farm.

keshavgandhi04 keshavgandhi04 · Answer 2 · 2021-12-07T12:16:12+01:00

The number of chicken are 32 and the number of cows is 16, 128 represents the total number of legs of the chicken and cows. In which 64 legs are of chicken and 64 legs are of cows, and 48 represents the total number of heads in which 32 heads are of chicken and 16 heads are of cows.

Given :

Farmer John has cows and chickens on his farm. His farm animals have 128 legs and 48 heads in total.

a) Remember a cow has one head and 4 legs and a chicken has one head and 2 legs.

Let the total number of chickens be 'x' and the total number of cows be 'y'. Then the total number of heads are:

x + y = 48

x = 48 - y --- (1)

The linear equation that represents the total number of legs is given by:

2x + 4y = 128 --- (2)

Now, substitute the value of 'x' in equation (2).

2(48 - y) + 4y = 128

96 - 2y + 4y = 128

2y = 32

y = 16

Now, substitute the value of 'y' in equation (1).

x = 48 - 16

x = 32

So, the number of chicken are 32 and the number of cows are 16.

b) 128 represents the total number of legs of the chicken and cows. In which 64 legs are of chicken and 64 legs are of cows.

c) 48 represents the total number of heads in which 32 heads are of chicken and 16 heads are of cows.

For more information, refer to the link given below:

https://brainly.com/question/11897796