We can represent their respective salaries as follows:

Gary's salary#=x#

Alexis's salary#=2 1/2xxx=5/2xxx=(5x)/2#

James's salary#=(x+18)#

Their total daily salary is #306#, so we can write:

#x+(5x)/2+(x+18)=306#

Open the brackets and simplify.

#x+(5x)/2+x+18=306#

#2x+(5x)/2+18=306#

Multiply all terms by #2# and then simplify.

#(2xx2x)+(2xx(5x)/2)+(2xx18)=306xx2#

#(4x)+(1cancel2xx(5x)/(1cancel2))+(36)=612#

#4x+5x+36=612#

#9x+36=612#

Subtract #36# from each side.

#9x+36-36=612-36#

#9x=576#

Divide both sides by #9#.

#(9x)/9=576/9#

#(1cancel9x)/(1cancel9)=64#

#x=64#

Thus, Gary's daily salary is #$64#.

Alexis's salary#=(5x)/2=(5xx64)/2=(5xx32cancel64)/(1cancel2)=5xx32=160#

Thus, Alexis's salary is #$160#.

James's salary#=(x+18)=(64+18)=82#

Thus, James's salary is #$82#.

To check:

#64+160+82=306#