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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).

Verified Answer :

the manager is 42
Kirk I'd 28
Matt is 20
and Brian is only 16

Answer:

Kirk's age is 28 years.

The manager's age is 24 years.

Brian's age is 36 years.

Matt's age is 18 years.

Step-by-step explanation:

Let Kirk's age be = a

Let manager's age be = b

Let Brian's age be = c

Let Matt's age be = d

The first clue is that when added together, their ages total 106 years.

\(a+b+c+d=106\)        .......(1)

Kirk is twice ten years less than the manager’s age.

\(a=2(b-10)\)    ..... (2)

Brian is 12 years younger than twice the manager’s age.

\(c=2b-12\)     ......(3)

Matt is 6 years older than half the manager’s age.

\(d=(b/2)+6\)       ......(4)

\(2(b-10)+b+2b-12+(b+12)/2=106\)

=> \(2b-20+b+2b-12+(b+12)/2=106\)

=> \((4b-40+2b+4b-24+b+12)/2=106\)

=> \((11b-52)/2=106\)

=> \((11b-52)=106*2\)

=> \(11b-52=212\)

=> \(11b=264\)

b = 24

\(d=(24/2)+6\)

d = 18

\(a=2(24-10)\)

a = 28

\(c=2(24)-12\)

c = 36

Lets check: \(a+b+c+d=106\)

\(28+24+36+18=106\)

=> \(106=106\)   (checked)

Kirk's age is 28 years.

The manager's age is 24 years.

Brian's age is 36 years.

Matt's age is 18 years.