system equitation

Question

Sammy asked the zookeeper how many birds and lions the zookeeper feeds. The zookeeper answered that there are 14 heads and 44 feet. How many of each animal does the zookeeper feed? Use 

Answer 1

As a Bird and Lion each have only one head, then the number of Birds and the number of Lions together must equal the number of heads, which is 14:

B+L=14

A Bird has 2 feet and a Lion has 4 feet, so the number of feet must equal 2 times the number of birds and 4 times the number of Lions:

2B+4L=44

 

Now we choose to use either substitution or elimination. I think it would be easiest to use substitution. I will start by rearranging our first equation:

B+L=14

   -L   -L

B=14-L

 

We can now substitute this value of B into our second equation:

2(14-L)+4L=44

 

This got us to an equation that only has one variable, making in possible to solve. I will start by distributing the 2:

28-2L+4L=44

Combine like terms:

28+2L=44

-28     -28

2L=16

/2   /2

L=8

 

Now we can substitute in our value for L into any of our equations to find B, I will use B=14-L because it is the most direct on finding B:

B=14-8

B=6

 

So you get that there are 8 Lions and 6 Birds