Respuesta :
Answer:
Kirk is 28 years old, Brian is 36 years old, Matt is 18 years old, and the manager is 24 years old.
Step-by-step explanation:
Let [tex]k[/tex] be Kirk's age.
Let [tex]b[/tex] be Brian's age.
Let [tex]m[/tex] be Matt's age.
Let [tex]m_{1}[/tex] be the boss/manager's age.
From the information given, we can set up 4 equations:
[tex]k+b+m+m_{1}=106[/tex]
[tex]k=2(m_{1}-10)[/tex]
[tex]b=2m_{1}-12[/tex]
[tex]m=\frac{1}{2}m_{1}+6[/tex]
Rewrite the first equation, substituting [tex]k[/tex], [tex]b[/tex], and [tex]m[/tex] in terms of [tex]m_{1}[/tex] to get:
[tex]2(m_{1}-10)+(2m_{1}-12)+(\frac{1}{2}m_{1}+6)+m_{1}=106[/tex]
Open up the parentheses using the distributive property (which is [tex]a(b-c)=ab-ac[/tex]) and combine like terms to get:
[tex]5.5m_{1}-26=106[/tex]
Add 26 to both sides to reach:
[tex]5.5m_{1}=132[/tex]
Thus, [tex]m_{1}=24[/tex]. Substitute [tex]24[/tex] for [tex]m_{1}[/tex] in the second, third, and fourth original equations to find that [tex]k=28[/tex], [tex]b=36[/tex], and [tex]m=18[/tex]. Therefore, Kirk is 28 years old, Brian is 36 years old, Matt is 18 years old, and the manager is 24 years old. To check, you can add up all of the ages to get 106.
Hope this helps :)
