There is a competition at the local movie theater for free movie tickets. You must guess all four employees' ages given a few clues. The first clue is that when added together,
their ages total 106 years. Kirk is twice ten years less than the manager's age, Brian is 12
years younger than twice the manager's age, and Matt is 6 years older than half the
manager's age. What are all four of their ages? It may help to set up four let statements,
one for each employee (including the manager).

Manager = 24

Kirk = 28

Brian = 36

Matt =18

Step-by-step explanation:

Let

The managers age = x

Kirk is twice ten years less than the manager's age

Kirk = 2(x - 10)

Brian is 12 years younger than twice the manager's age

Brian = 2x - 12

Matt is 6 years older than half the

manager's age.

Matt = 1/2x + 6

Total = 106 years

Add the four employees ages

x + 2(x-10) + (2x-12) + (1/2x + 6) = 106

x + 2x - 20 + 2x - 12 + 1/2x + 6 = 106

5x + 1/2x - 26 = 106

10x+x/2 = 106 + 26

11/2x = 132

x = 132 ÷ 11/2

= 132 × 2 / 11

= 264 / 11

= 24

x = 24

Managers age = x = 24 years

Kirk = 2(x - 10)

= 2(24 - 10)

= 2(14)

= 28 years

Brian = 2x - 12

= 2(24) - 12

= 48 - 12

= 36 years

Matt = 1/2x + 6

= 1/2(24) + 6

= 12 + 6

= 18 years

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