Question

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 when their ages are added together the sum is Kirk is 2 times the quantity of 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 ½ the manager's age. What are all four of their ages? Be sure to show set up equation work and answer

Answer 1

Complete question :

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 when their ages are added together the sum is 106. Kirk is 2 times the quantity of 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 ½ the manager's age. What are all four of their ages? Be sure to show set up equation work and answer

Answer:

Kindly check explanation

Step-by-step explanation:

Given the following clue :

Let manager's age = m

Kirk's age = k

Brian's age = b

Matt's age = a

Sum of their ages = 106

k = 2(m - 10) = 2m - 20

b = 2m - 12

a = 0.5m + 6

k + b + a + m = 106

Express all their ages in terms of m

2m - 20 + 2m - 12 + 0.5m + 6 + m = 106

5.5m - 20 - 12 + 6 = 106

5.5m - 26 = 106

5.5m = 106 + 26

5.5m = 132

m = 132 / 5.5

m = 24

Manager's age = 24 years

kirk = 2(24 - 10) = 2(14) = 28 years

Brian = 2(24) - 12 = 48 - 12 = 36 years

Matt = 0.5(24) + 6 = 12 + 6 = 18 years