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.
Let be Brian's age.
Let be Matt's age.
Let be the boss/manager's age.
From the information given, we can set up 4 equations:
Rewrite the first equation, substituting ,
, and
in terms of
to get:
Open up the parentheses using the distributive property (which is ) and combine like terms to get:
Add 26 to both sides to reach:
Thus, . Substitute
for
in the second, third, and fourth original equations to find that
,
, 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.
Hope this helps :)