Let the volunteering hours of each sibling be

'x' the hours that Dave volunteered

'y' the hours that Kate volunteered

'z' the hours that Sara volunteered

z = x + 15 (Sara worked 15 hours more than Dave)

y = x - 5 (Kate worked 5 hours fewer than Dave)

x + y + z = 100 (Dave, Kate and Sara committed themselves to volunteer 100 hours)

The solutions of the following system of 3 equation are the hours that each sibling volunteered:

z = x + 15

y = x - 5

x + y + z = 100

that is

x + x - 5 + x + 15 = 100

3x = 90

x = 30

y = x - 5 = 30 - 5 = 25

z = x + 15 = 30 + 14 = 45

Dave volunteered 30 hours, Kate volunteered 25 hours and Sara volunteered 45 hours.