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An employment agency specializing in temporary construction help pays heavy equipment operators
$130 per day and general laborers
$93 per day. If thirty-four people were hired and the payroll was
$3717, how many heavy equipment operators were employed? How many laborers?

An employment agency specializing in temporary construction help pays heavy equipment operators $\$ 130$ per day and general laborers $\$ 93$ per day. If thirty-four people were hired and the payroll was $\$ 3717$ , how many heavy equipment operators were employed? How many laborers?

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Add and subtract money amounts: word problems

Full solution

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

\$ 130

per day and general laborers

\$ 93

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

\$ 3717

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

Define variables: Step $1$ : Define the variables for the number of heavy equipment operators and laborers. $\newline$ Let $x$ be the number of heavy equipment operators. $\newline$ Let $y$ be the number of general laborers. $\newline$ Total number of people hired: $x + y = 34$
Set up payroll equation: Step $2$ : Set up the equation for the total payroll. $\newline$ Pay for heavy equipment operators: $\$130$ per day. $\newline$ Pay for laborers: $\$93$ per day. $\newline$ Total payroll equation: $130x + 93y = \$3717$
Solve system of equations: Step $3$ : Solve the system of equations. $\newline$ From Step $1$ : $y = 34 - x$ . $\newline$ Substitute $y$ in the payroll equation: $\newline$ $130x + 93(34 - x) = 3717$ $\newline$ $130x + 3162 - 93x = 3717$ $\newline$ $37x + 3162 = 3717$ $\newline$ $37x = 3717 - 3162$ $\newline$ $37x = 555$ $\newline$ $x = \frac{555}{37}$ $\newline$ $x = 15$
Find values of x and y: Step $4$ : Find the value of y using $x = 15$ . $\newline$ $y = 34 - 15$ $\newline$ $y = 19$

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