Question

The Martins keep goats and chickens on their farm. If there are 23 animals with a total of 74 legs, how many of each type of animal are there? Let the number of chickens be c Then the number of goats in terms of c is (23 – c) State in algebraic terms: the total number of legs the chickens have ___________________________ (1)2c the total number of legs the goats have _____________________________(2)4c Write an algebraic equation in terms of c to represent the total number of animal legs (74 legs) on the farm. (3) 23-c=74 Hence solve the algebraic equation and calculate the number of goats and chickens on the farm.(4)

Answer 1

The Martins' farm has 9 chickens and 14 goats, determined by solving the equation 2c + 4(23 - c) = 74 where 'c' represents the number of chickens.

Step-by-step explanation:

The question involves setting up and solving systems of equations to determine the number of chickens (c) and goats (23 - c) on the Martins' farm. Since chickens have 2 legs each and goats have 4 legs each, we can represent the total number of legs chickens have algebraically as 2c, where 'c' represents the number of chickens. Similarly, the total number of legs that the goats have can be represented as 4(23 - c), as there are 23 - c goats and each goat has 4 legs.

To set up an equation that represents the total number of animal legs (74 legs) on the farm, we add the two expressions together:

2c + 4(23 - c) = 74

Now we solve for 'c':

1. Distribute the 4 in the goat's expression: 2c + 92 - 4c = 74
2. Combine like terms: -2c + 92 = 74
3. Subtract 92 from both sides: -2c = -18
4. Divide both sides by -2: c = 9

Since there are a total of 23 animals, and 'c' represents the number of chickens, the number of chickens is 9, and the number of goats is 23 - 9 = 14.

Answer 2

There are 9 chickens and 14 goats on the farm.

Let c be the number of chickens. Since there are 23 animals in total, the number of goats is 23 - c

1. The total number of legs the chickens have is 2c.

2. The total number of legs the goats have is 4 (23 - c), because each goat has 4 legs.

3. The algebraic equation to represent the total number of animal legs (74 legs) on the farm is given by the sum of the legs of chickens and goats:

`\[2c + 4(23 - c) = 74.\]`

Now, let's solve this equation:

`\[2c + 92 - 4c = 74.\]`

Combine like terms:

`\[-2c + 92 = 74.\]`

Subtract 92 from both sides:

`\[c = 9.\]`
`\[-2c = -18.\]`

Divide by -2:

`\[c = 9.\]`

Now that we know \(c = 9\), we can find the number of goats (\(23 - c\)):

`\[23 - 9 = 14.\]`