These problems are hard to solve because sometimes students don't realize that they need two kinds of data
• The #"number"# of each type of employee
• The #"wage value"# of each type of employee
#color(white)(.............)――――――#
Find a way to express the #"number"# of each type of employee
Let #x# represent the number of heavy equipment operators
Operators . . . #x# #larr# the #"number"# of heavy equipment operators
Laborers . . #(31 - x)# #larr# The #"number"# of general laborers
#color(white)(..................)――――――#
Find a way to express the #"wage value"# of each type of employee
#color(white)(.)##x# heavy equipment operators @ #$140# ea = #$140x# #larr# the #"value"# of their wages
#(31 - x)# general laborers @ #$95# ea = #$95(31-x)# #larr# the #"value"# of their wages
#color(white)(..................)――――――#
All together, these #"wage values"# add up to #$3620#
[operators' wages] + [ laborers' wages} = #$3620#
[ #color(white)(.........)##140x##color(white)(.......)#] + [ #color(white)(...)##95(31-x)# #color(white)(.)# ] = #3620#
#140x + 95(31-x) = 3620#
#color(white)(..................)――――――#
Solve for #x#, already defined as "the number of heavy equipment operators
#140x + 95(31-x) = 3620#
1) Clear the parentheses
#140x + 2945 - 95x = 3620#
2) Combine like terms
#45x + 2945 = 3620#
3) Subtract 2945 from both sides to isolate the #45x# term
#45x = 675#
4) Divide both sides by #45# to isolate #x#, already defined as "the number of heavy equipment operators"
#x = 15#
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#"Answer:"#
There were #15# heavy equipment operators
(and therefore #16# general laborers)
#color(white)(..................)――――――#
Check
15 equipment operators @ $140 ea .... $2100
16 general laborers #color(white)(.....)# @ $ 95 ea......$1520
―――――――――#color(white)(..)##color(white)(.......................)#―――
31 people #color(white)(........................................)# $3620
#Check#
