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#
