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
