Hi,
Let x represent Mike's age...then
David is(x+5)
sheila is (x+6)
nancy is (x+9)
claire is (x+10)
Question states***
x + (x+5)+(x+6)+(x+9)+(x+10) = 120
5x +30 = 120
5x = 90
x = 18, Mike's age. David 23, Sheila 24, Nancy 27 and Claire 28
CHECKING our Answer***
18 + 23 + 24 + 27 + 28 = 120