College algebra

Question

An employment agency specializing in temporary construction help pays heavy equipment operators $121 per day and general laborers $98 per day. If forty people were hired and the payroll was $4472, how many heavy equipment operators were? employed? How many? laborers?

Answer 1

We'll start by calling the heavy equipment operators 'x'

and the general laborers 'y'

 

We know, altogether, there are 40 workers. That means the heavy equipment operators plus the general laborers.

So this gives us the first equation x + y = 40.

 

We also know the total payroll is $4472 for the heavy equipment operators (who make $121/dy) and the general laborers (who makemake $98/dy). 

So this gives us the second equation 121x + 98y = 4472

 

x + y = 40

121x + 98y = 4472

 

This is now a system of equations (just means more than one equation to solve for and that the equations are related in some way).

 

A system of equations can be solved by 1) Substitution, 2) Addition, or 3)Using the Graphing Calculator.

I will use substitution.

 

Step 1: Transform the 'smaller' equation (just means rearranging it for one of the variables)

     x + y = 40

     x + y - y = 40 - y

     x = 40 - y

(did we actually solve for anything? No, but we need this new rearranged equation to substitute it into the other equation)

 

Step 2: Place the new rearranged equation into the second equation

     121x + 98y = 4472

     121(40 - y) + 98y = 4472   

     4840 - 121y + 98y = 4472  (we used the distributive property)

     4840 - 23y = 4472    (we combined like terms on the SAME side of the equation)

     4840 - 4840 - 23y = 4472 - 4840   (we moved the 4840 to the OPPOSITE side of the equation)

     -23y = -368  

     -23y⁄-23 = -368⁄-23    (we moved the -23 to the OPPOSITE side of the equation)

     y = 16

 

Now we have a value we can use to answer the question in the word problem....

 

'y' represented the general laborers; which we now know there are 16 of them.

 

And we also know there is a total number of 40 workers including both general laborers and heavy equipment operators.

 

This means 40 - 16 = 24 heavy equipment operators.

 

ANSWER: 16 general laborers and 24 heavy equipment operators