Let [tex]x[/tex] be the number of heavy equipment operators, and [tex]y[/tex] the number of general laborers.
We know for our problem that total number of workers is 39, so [tex]x+y=39[/tex] equation (1). We also know that the construction firm pays heavy equipment operators $137 per day and general laborers $86 per day and the total payroll was $4680, so [tex]137x+86y=4680[/tex] equation (2).
Solve for [tex]x[/tex] in equation (1)
[tex]x+y=39[/tex]
[tex]x=39-y[/tex] equation (3)
Replace equation (3) in equation (2)
[tex]137x+86y=4680[/tex]
[tex]137(39-y)+86y=4680[/tex]
[tex]5343-137y+86y=4680[/tex]
[tex]-51y=-663[/tex]
[tex]y= \frac{663}{51} [/tex]
[tex]y=13[/tex] equation (4)
Replace equation (4) in equation (3)
[tex]x=39-y[/tex]
[tex]x=39-13[/tex]
[tex]x=26[/tex]
We can conclude that the number of heavy operators hired was 26, and the number of general laborers hired was 13.
