# A local kennel has twice as many cats (c) as dogs (d).  When full the kennel has a total of 30 cats and dogs.  Write a system of equations that could be used to find the number of cats in the...

A local kennel has twice as many cats (c) as dogs (d).  When full the kennel has a total of 30 cats and dogs.  Write a system of equations that could be used to find the number of cats in the kennel when it is full. Do not solve.

crmhaske | College Teacher | (Level 3) Associate Educator

Posted on

Let c = the number of cats in the kennel
Let d = the number of the dogs in the kennel

There are twice as many cats as dogs:  c = 2*d

When full, the total number of animals in the shelter is 30: 30 = c + d

Therefore, the two equations required to solve this problem are:

c = 2*d
30 = c + d

In order to solve for the number of cats, you must sub the first equation into the second equation.  Now you can solve for the number of dogs.  With this information you can determine the number of cats in the kennel when it is full by multiplying the number of dogs by 2.

Sources: