the sum of three consecutive even intergers is 198. find the intergers

Question

my professor didn't exactly explain this properly- he breezed through it a few different times and i haven't exactly been able to follow his steps. i was wondering if there would be a way for this to be shown step by step to see how to get the intergers or how to figure out which intergers equal 198.

Answer 1

Let the 1st integer = x

Let the 2nd integer = x + 2

Let the 3rd integer = x + 4

 

Using these variables, set the equation to represent the sum of these integers.

 

x + (x + 2) + (x + 4) = 198

 

 

Solve for x from this equation.  Can you do it now?

Answer 2

Hi Brittany,

 

Let's say that one of the consecutive even integers is n. That means that the next two are (n + 2) and (n + 4), for simplicity's sake. You can also say that the other two are (n - 2) and (n - 4) or that they are (n - 2) and (n + 2), but they would all give you the same numbers in the end.

 

So if three consecutive even integers add up to 198:

 

n + (n + 2) + (n + 4) = 198

 

We can solve for n:

 

3n + 6 = 198

 

3n = 192

 

n = 64

 

The other two integers are then (n + 2) = 66 and (n + 4) = 68.

 

Hope this helps!