Question

Pls help this is due today

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.

c. 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.

Answer:

Part A)

Part B)

Part C)

Part D

Answer 1

The total number of legs of the cows and chickens combined is represented by 128, and the total number of heads is represented by 48. By setting up a system of equations, we can solve for the number of cows and chickens. Using the substitution method, we find that there are 16 cows and 32 chickens on the farm.

Step-by-step explanation:

Part A:

In the problem, 128 represents the total number of legs of the cows and chickens combined. Since cows have 4 legs and chickens have 2 legs, let's represent the number of cows as 'C' and the number of chickens as 'Ch'.

Now, we can set up an equation: 4C + 2Ch = 128.

Part B:

48 represents the total number of heads of the cows and chickens combined. Since each animal has one head, the number of cows and chickens together is represented by 'C + Ch'.

The equation for this is: C + Ch = 48.

Part C:

We have two unknowns (C and Ch) and two equations. We can set up a system of equations:

4C + 2Ch = 128 (Equation 1)

C + Ch = 48 (Equation 2)

Part D:

To solve this system, we can use the method of substitution. From Equation 2, we can isolate one of the variables:

C = 48 - Ch

Now we substitute this value of C into Equation 1:

4(48 - Ch) + 2Ch = 128

After simplifying, we get:

192 - 4Ch + 2Ch = 128

-2Ch = -64

Ch = 32

Substituting this value of Ch back into Equation 2, we can find the value of C:

C + 32 = 48

C = 16

Therefore, there are 16 cows and 32 chickens on the farm.

Answer 2

There are 16 cows and 32 chickens on the farm.

Step-by-step explanation:

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.

Step-by-step explanation: