Answer:
Kirk is <u>28</u> years old, Brian is <u>36</u> years old, Matt is <u>18</u> years old, and the manager is <u>24</u> years old. 
Step-by-step explanation:
Let  be Kirk's age.
 be Kirk's age.
Let  be Brian's age.
 be Brian's age.
Let  be Matt's age.
 be Matt's age.
Let  be the boss/manager's age.
 be the boss/manager's age.
From the information given, we can set up 4 equations:
 



Rewrite the first equation, substituting  ,
,  , and
, and  in terms of
 in terms of  to get:
 to get:

Open up the parentheses using the distributive property (which is  ) and combine like terms to get:
) and combine like terms to get:

Add 26 to both sides to reach:

Thus,  . Substitute
. Substitute  for
 for  in the second, third, and fourth original equations to find that
 in the second, third, and fourth original equations to find that  ,
,  , and
, and  . Therefore, Kirk is <u>28</u> years old, Brian is <u>36</u> years old, Matt is <u>18</u> years old, and the manager is <u>24</u> years old. To check, you can add up all of the ages to get 106.
. Therefore, Kirk is <u>28</u> years old, Brian is <u>36</u> years old, Matt is <u>18</u> years old, and the manager is <u>24</u> years old. To check, you can add up all of the ages to get 106.
Hope this helps :)