Algebra word problem

Question

An employment agency pays heavy equipment operators $120 per day and general laborers $86 per day. If thirty-five people were hired and the payroll was $3690, how many heavy operators were employed? How many laborers?

Answer 1

The first step is to assign variables.  We can use x to represent the number of heavy equipment operators, and y to represent the number of general laborers.

 

We know that thirty-five people were hired, so the general laborers and the heavy equipment operators together must total thirty-five, or

x + y = 35.

 

The payroll, in this case, refers to the total cost per day.  They have to pay $120 per heavy equipment operator per day, or 120x, and $86 per general laborer per day, or 86y, so the total payroll of $3690 implies

120x + 86y = 3690

 

Solving these two equations can tell us the values of x and y.  Particularly, let's rearrange the first equation:

y = 35 - x

And substitute into the second

120x + 86(35 - x) = 3690

120x + 3010 - 86x = 3690

34x = 680

x = 20

 

Substitute this into the rearranged equation above

y = 35 - 20 = 15

 

So we have 20 heavy equipment operators and 15 general laborers.  Check that this works:

 

15 + 20 = 35 people, as expected.

20 * $120 + 15 * $86 = $2400 + $1290 = $3690, as expected.  Our answer works.