an employment agency specializing in temporary construction help pays heavy equipment operators $133 per day and general laborers $81 per day. if thirty people were hiredand the payroll was $3314 how many heavy equipment operators were employed? how many laborers?

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carlosego carlosego · Answer 1 · 2018-09-08T17:45:51+02:00

For this case, the first thing we must do is define variables.

We have then:

x: number of heavy equipment operators

y: number of general laborers

We write the system of equations that models the problem:

[tex] 133x + 81y = 3314 [/tex]

[tex] x + y = 30 [/tex]

From here, we clear the value of the unknowns.

From equation two we have:

[tex] y = 30-x [/tex]

Substituting in equation 1 we have:

[tex] 133x + 81 (30-x) = 3314 [/tex]

[tex] 133x-81x + 2430 = 3314 [/tex]

[tex] 52x = 3314-2430 [/tex]

[tex] 52x = 884 [/tex]

[tex] x = 17 [/tex]

Then, the value of y is:

[tex] y = 30-x [/tex]

[tex] y = 30-17 [/tex]

[tex] y = 13 [/tex]

Answer:

were employed:

heavy equipment operators: 17

general laborers: 13