An employment agency specializing in temporary construction help pays heavy equipment operators $\$ 124$ per day and general laborers $\$ 99$ per day. If thirty-three people were hired and the payroll was $\$ 3817$ , how many heavy equipment operators were employed? How many laborers?

Full solution

Q. An employment agency specializing in temporary construction help pays heavy equipment operators

\$ 124

per day and general laborers

\$ 99

per day. If thirty-three people were hired and the payroll was

\$ 3817

, how many heavy equipment operators were employed? How many laborers?

Set up equations: Step $1$ : Set up the equations based on the given information. $\newline$ Let $x$ be the number of heavy equipment operators and $y$ be the number of general laborers. $\newline$ Equation $1$ : $x + y = 33$ (since $33$ people were hired) $\newline$ Equation $2$ : $124x + 99y = 3817$ (total payroll calculation)
Solve for $y$ : Step $2$ : Solve the first equation for $y$ . $y = 33 - x$ Substitute $y$ in Equation $2$ : $124x + 99(33 - x) = 3817$
Simplify and solve for $x$ : Step $3$ : Simplify and solve for $x$ . $124x + 3237 - 99x = 3817$ $25x + 3237 = 3817$ $25x = 3817 - 3237$ $25x = 580$ $x = \frac{580}{25}$ $x = 23.2$