Gregg manages a small cleaning business. He has 18 employees. The cleaners get paid $14.00per hour. The cleaning supervisors get paid $19.00 per hour. His budget has set aside a payroll expense of $282.00 per hour if all of his employees are working. How many cleaners and how many supervisors does he employ? Gregg employed
nothing cleaners and
nothing supervisors.

Gregg employed 12 cleaners and 6 cleaning supervisors.

Step-by-step explanation:

Set up a system of equations where c is the number of cleaners and s is the number of cleaning supervisors:

c + s = 18

14c + 19s = 282

Solve by substitution by solving for c in the first equation:

c + s = 18

c = 18 - s

Then, plug in 18 - s as c into the second equation:

14c + 19s = 282

14(18 - s) + 19s = 282

Solve for s:

252 - 14s + 19s = 282

252 + 5s = 282

5s = 30

s = 6

Then, plug in 6 as s into the first equation:

c + s = 18

c + 6 = 18

c = 12

So, Gregg employed 12 cleaners and 6 cleaning supervisors.