let

x = the hours per week that Katie volunteers

y = the hours per week that Elizabeth volunteers

z = the hours per week that Shannon volunteers

in a week Katie volunteers 3 hours more than Elizabeth:

x = 3 + y

Shannon volunteers 1 hour less than Elizabeth does:

z = y - 1

over 3 weeks the number of hours Katie volunteers is equal to Shannon and Elizabeth:

3x = 3(y + z) divide both sides by 3

x = y + z

by solving the system of equations:

x = 3 + y

z = y - 1

x = y + z

we find:

x = 7 hr

y = 4 hr

z = 3 hr

click here to see the step by step solution of the system of equations:

Katie volunteers 7 hours per week.

Elizabeth volunteers 4 hours per week.

Shannon volunteers 3 hours per week.