Question

There is a competition in the cinema to win free tickets. You must guess the ages of the four employees. Here are the clues: - When you add up all the ages, the total is 106; Kirk is twice the age difference of "manager" and 10; Brian is 12 years younger than twice the manager's age; Matt is 6 years older than half the manager's age. (the "manager" is like the boss or manager). What are all the ages of the four employees? Make four "Let" phrases, one for each employee (including the manager) *

Answer 1

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 $k$ be Kirk's age.

Let $b$ be Brian's age.

Let $m$ be Matt's age.

Let $m_{1}$ be the boss/manager's age.

From the information given, we can set up 4 equations:

$k+b+m+m_{1}=106$

$k=2(m_{1}-10)$

$b=2m_{1}-12$

$m=\frac{1}{2}m_{1}+6$

Rewrite the first equation, substituting $k$, $b$, and $m$ in terms of $m_{1}$ to get:

$2(m_{1}-10)+(2m_{1}-12)+(\frac{1}{2}m_{1}+6)+m_{1}=106$

Open up the parentheses using the distributive property (which is $a(b-c)=ab-ac$) and combine like terms to get:

$5.5m_{1}-26=106$

Add 26 to both sides to reach:

$5.5m_{1}=132$

Thus, $m_{1}=24$. Substitute $24$ for $m_{1}$ in the second, third, and fourth original equations to find that $k=28$, $b=36$, and $m=18$. 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 :)