How many of each?

Question

An employment agency specializing in temporary construction help pays heavy equipment operators $136

per day and general laborers $87 per day. If 33 people were hired and the payroll was $4390,

how many heavy equipment operators were​ employed? How many​ laborers?

Answer 1

To solve by Elimination:

h = heavy equipment operators

g = general laborers

136h + 87g = 4390

87h + 87h = 2871 [from 87 * (h + g = 33) ]

--------------------------- [Elimination: subtract]

49h = 1419

h = 31 [divide both sides by 49]

h+g=33

h = 31

--------------- [Elimination: subtract]

g = 2

Answer 2

Let h=heavy equipment operators

and g=general laborers

h+g=33

Subtract h from both sides to get

g=33-h

136h+87g=4390

Substitute 33-h for g

136h + 87(33-h)=4390

Distribute

136h +2871-87h=4390

Combine like terms

49h+2871=4390

Subtract 2871 from both sides

49h=1519

Divide both sides by 49

h=31 (heavy equipment operators)

Since g=33-h=33-31=2 (general laborers)