Question

2. a chicken farmer also has some cows for a total of 30 animals and the animals have 74 legs in all. how many chickens does the farmer have? 23

Answer 1

23 chickens

Explanation:

x + y = 30

We also know that the total number of legs is 74. Each chicken has 2 legs, and each cow has 4 legs, so we can write:

2x + 4y = 74

Now we have two equations with two variables, and we can solve for x (the number of chickens). We can start by solving the first equation for y:

y = 30 - x

Substituting this into the second equation, we get:

2x + 4(30 - x) = 74

Simplifying this equation, we get:

-2x + 120 = 74

Subtracting 120 from both sides, we get:

-2x = -46

Dividing both sides by -2, we get:

x = 23

So, there are 23 chickens.

Answer 2

23 chickens

Explanation:

Step 1: Set Up a System of Equations

We know that this farmer has some unknown amount of chickens, and some unknown amount of cows. Let's assign a letter to each unknown variable - let the number of chickens be c, and the number of cows be w.

The problem tells us that the farmer has a total of 30 animals (cows and chickens together). Therefore, c + w = 30.

We are then given some information about how many legs the animals have. Recall that a chicken has 2 legs and a cow has 4. Since (we are assuming that) each animal has the "normal" number of legs, we can represent the number of chicken legs as 2c and the number of cow legs as 4w. Since the animals have 74 legs in all, we know that 2c + 4w = 74.

Step 2: Solve the System

We now have the following system of equations:

c + w = 30 (1)

2c + 4w = 74 (2)

The problem is asking us to find the number of chickens, or c. Note that this means we do not have to find the number of cows, or w, so let's manipulate the system to eliminate w, which will make solving for c easier. Solving, we get:

4c + 4w = 120 (3) (Multiply (1) by 4)

2c = 46 (Subtract (2) from (3))

c = 23 (Divide by 2)

Thus, the farmer has 23 chickens.