I need help with this word problem

Question

An employment agency specializing in temporary construction help pays heavy equipment operators $123 per day and general laborer a $98 per day. If forty people were hired and the payroll was $4470, how many heavy equipment operators were employed? How many laborers?

Answer 1

Hi Nia,

 

    The hardest part of problems like these is getting the words into math equations and symbols.  Let me help you with that part, and I'll leave the rest to you.

 

    We want to know the numbers of heavy equipment operators and laborers, so let's assign math symbols to each one of those.  We'll call the number of heavy equipment operators "X" and we'll call the number of general laborers "Y".  If the total number of employees is 40, then we can express this mathematically as:

 

            X + Y = 40

 

    What else do we know?  We know that in 1 day the company pays out 4470 dollars and that they pay different rates for each type of worker.  If we multiple the number of workers by their pay, we'll get the companies pay out.  This gives us:

 

            123X + 98Y = 4470

 

    I'll leave the algebra to you.  (HINT: you can either add multiples of the equation together to eliminate one of the variables, OR you can solve this problem using a matrix.  It all depends on what unit you are in in your course.)