SOLUTION: a union contract requires at least one union steward for every 20 union employees or fraction thereof. regular union employees ear $120/day and union stewards earn $144/day. a comp

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Question 256112: a union contract requires at least one union steward for every 20 union employees or fraction thereof. regular union employees ear $120/day and union stewards earn $144/day. a company has a need for 50 total employees and has a daily payroll budget of $6072. how many of each type of employee will meet the company's needs and consume all the budget?
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
a union contract requires at least one union steward for every 20 union employees or fraction thereof. regular union employees earn $120/day and union stewards earn $144/day. a company has a need for 50 total employees and has a daily payroll budget of $6072. how many of each type of employee will meet the company's needs and consume all the budget?
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Quantity Equation: e + (e/20) = 50
Value Equation: 120e + 144(e/20) = 6072
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Multiply thru the Quantity equation by 120:
120e + 6e = 120*50
120e + 144(e/20) = 6072
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Subtract the 1st Eq. from the 2nd and solve for "e":
144(e/20)- 6e = 72
144e - 120e = 72*20
24e = 72*20
e = 3*20
e = 60
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But there must be 1 steward for each 20 employees or fraction thereof
and only 50 personnel are to be hired.
So # of stewards is 3 and number of employees is 47
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Checking:
120*47 + 144*3 = $6072
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Cheers,
Stan H.

Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
Let = number of union stewards
Let = number of union employees
given:
(1)
(2)
(3)
From (2),
From (1),

And, from (2) again,

From (3)

All conditions are satisfied if there are 3 stewards and 47 union employees