Solving a word problem for college algebra

Question

An employment agency specializing in temporary construction help pays heavy equipment operators $139 per day and general labors $97 per day. If 39 people were hired and payroll was $4875, how many heavy equipment operators were employed? How many laborers?

Answer 1

h = # heavy equipment operators

g = # general laborers

 

from information you can make two equations:

1).  h + g = 39    total people hired

2).  139h + 97g = 4875.  total payroll is $4875

 

in equation 1 solve for h in terms of g

h = 39-g

 

in equation 2 replace h with 39-g

139(39-g) + 97g = 4875

 

solve for g to determine number of general laborers

 

subtract g from 39 to find h.

 

Answer 2

h = heavy equipment

g = general labor

 

$139h + $97g = $4875

h + g = 39

 

1) Isolate a variable.

 

h = 39-g

 

2) Plug into equation 1.

 

139(39-g) + 97g = 4875

5421 - 139g + 97g = 4875

-42g = -546

g = 13

 

3) Now solve for h.

 

h = 39 - 13

h = 26

 

4) Check your work on equation 1.

 

139(26) + 97(13) = 4875

3614 + 1261 = 4875

4875=4875