Algebra 1 homework

Question

there is a competition at the local movie theater for free movie tickets. you must guess all employeesages give a few clues the first clue is that when added together their ages total 106 years. kirk is twice ten years less that the managers age. brian is 12 years younger than twice the managers age.and matt is 6 years older than half the managers age. what are all four of their ages

Answer 1

K = Kirk

B = Brian

M = Matt

X = manager

K + B + M + X = 106

K = 2(X - 10)

B = 2X - 12

M = 0.5X + 6

2(X - 10) + 2X - 12 + 0.5X + 6 + X = 106

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

5.5X - 26 = 106

5.5X = 132

X = 24

K = 2(24 - 10) = 2(14) = 28

B = 2(24) - 12 = 48 - 12 = 36

M = 0.5(24) + 6 = 12 + 6 = 18

28 + 24 + 36 + 18 = 106

Kirk is 28 years old. Brian is 36 years old. Matt is 18 years old. The manager is 24 years old.