let

x = the amount that Joe makes

y = the amount that Jessica makes

Joe makes 2/3 of what Jessica makes:

x = (2/3)y

Together they make 600:

x + y = 600

by solving the system of equations:

x = (2/3)y

x + y = 600

we find

x = $240

y = $360

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

Joe makes $240.

Jessica makes $360.