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

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?
----
Quantity Equation: e + (e/20) = 50
Value Equation: 120e + 144(e/20) = 6072
--------------------------
Multiply thru the Quantity equation by 120:
120e + 6e = 120*50
120e + 144(e/20) = 6072
--------------------------------
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
---
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
------
Checking:
120*47 + 144*3 = $6072
=============================
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
RELATED QUESTIONS
A union contract requires at least one union steward for every 20 union employees or... (answered by richwmiller)
What is a counter example for... (answered by tommyt3rd)
prove that this true or false? P(A union B) = P(A) union... (answered by stanbon)
A union worker made $500 a week. His Union sought a one year contract and went on strike. (answered by ankor@dixie-net.com)
A union worker made $500 per week. His union sought a one-year contract and went on... (answered by ReadingBoosters)
Regular union employees earn $120/day, and union stewards earn $144/day. a company has a... (answered by mananth)
The employees of Jones Construction Co. are allowed a 30-minute lunch break. The union... (answered by stanbon)
Taking an algorithm course and working a union-find problem. Algebra & trig too long ago (answered by ikleyn)
The union for a particular industry has determined that the standard deviation of the... (answered by stanbon)