laborers 125

Question

An employment agency specializing in temporary construction help pays heavy equipment operators
$ 125
per day and general laborers
$ 87
per day. If
38
people were hired and the payroll was
$ 4332
how many heavy equipment operators were? employed? How many? laborers?

Answer 1

If all laborers worked 1 full day, exactly, then let G = # of general labors ($87/day) and then 38-G = # of heavy equipment operators (at $125/day).

 

Income 4332 = 87G + 125(38-G)   do you see why?  Then solve for G.

Answer 2

Using variables, we may express the word (the story) of this problem in math expressions and equations.

 

Let:

    x = number of heavy equipment operators

    y = number of general laborers

 

Here is one equation that is pretty easy:

  "38  people were hired"   means

    38 = x + y             [eq1]

 

Now, use the fact that the amount paid to the groups x and y is:

     (pay rate for group)*(number of workers in the group)    

                 [that is, ($/numb)(numb) and numb cancels]

 

  Amt. paid to heavy equipment operators + amt. paid to general laborers = total amount paid

            $125*x                                      +                $87*y                   = $4332   [eq2]

 

Let's solve using the substitution method [solve for one variable using one equation, then substitute that into the other equation to solve for the other variable; then use either equation to get the value of the first variable]:

     x = 38-y             [from eq1]

     $125(38-y) + $87y = $4332           [put that into eq1]

        $4750 - $125y   + $87y  = $4332       [distribute]

         $418 = $38y          [add $135y and subtract $4750 from both sides]

         11 = y                [these problems usually have a whole number of people]

Now, put that into either equation (get the same answer either way); eq1 is easier:

       x + 11 = 38

       x = 27

 

There were 27 heavy equipment operators and 11 general laborers.

 

Now (very important), check!

  Is  27 + 11 = 38   ?

        38  =  38   ?yes

  Is  $125*27 + $87*11 = $4332   ?

         $3375 + $957 = $4332   ?

           $4332 = $4332   ?yes