Question

Read the following situation:

There are 13 animals in the barn. Some are chickens and some are pigs. There are 40 legs in all. How many of each animal are there?

When setting up the system, what could the variables represent? Select all that apply.

Total number of chicken legs

Total number of pigs

How long until the number of pigs and chickens are equal.

How many animals in the barn

Total number of pig legs

Total number of chickens

Where the lines cross

Answer 1

Hi, let's turn the word problem into a set of equations:

Let's say that x = # of chickens, and y = # of pigs

If there are 13 animals altogether, that means that

x + y = 13

If there are 40 legs together, we know that chickens have 2 legs, while pigs have 4, so the total number of legs would be:

2x + 4y = 40

We now have two different equations, with the same two variables, so we can rearrange and substitute one equation into the other to solve. We can rearrange the first equation as:

x + y = 13

x = 13 - y

Let's plug this expression for "x" into the second equation:

2(13-y) + 4y = 40

Now we have an equation with only one variable, so we can use algebra to solve for y:

26 - 2y + 4y = 40

2y = 14

y = 7, there must be 7 pigs.

From the first equation that we rearranged,

x = 13 - y

Now that we know the numerical value of "y", we can plug that in:

x = 13 - 7

x = 6, there must be 6 chickens