An employment agency in temporary construction help pays heavy equipment operators $140 per day and general laborers $90 per day. If thirty-five people were hired and the payroll was $3950, how many heavy equipment operators were employed? How many laborers?

Question
Algebra foundations
asked 2020-11-29
An employment agency in temporary construction help pays heavy equipment operators $140 per day and general laborers $90 per day. If thirty-five people were hired and the payroll was $3950, how many heavy equipment operators were employed? How many laborers?

Answers (1)

2020-11-30
Let x be the number of operators and y be the number of laborers.
Thirty-five people were hired so:
\(\displaystyle{x}+{y}={35}{\left({1}\right)}\)
The payroll was $3950 so:
\(\displaystyle{140}{x}+{90}{y}={3950}{\left({2}\right)}\)
Solve for yy using (1) to obtain (3):
\(\displaystyle{y}={35}−{x}{\left({3}\right)}\)
Substitute (3) to (2) and solve for x:
\(\displaystyle{140}{x}+{90}{\left({35}−{x}\right)}={3950}\)
\(\displaystyle{140}{x}+{3150}−{90}{x}={3950}\)
\(\displaystyle{50}{x}+{3150}={3950}\)
\(\displaystyle{50}{x}={800}\)
\(\displaystyle{x}={16}\)
Solve for y using (3):
\(\displaystyle{y}={35}−{16}\)
\(\displaystyle{y}={19}\)
So, there were 16 operators and 19 laborers.
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