SOLUTION: A business director awards his staff with gift cards of $10.00 value each. He gives 3 gift cards to employees who have been employed in his business for 3 years, 5 gift cards to e

Question 1132635: A business director awards his staff with gift cards of $10.00 value each. He gives 3 gift cards to employees who have been employed in his business for 3 years, 5 gift cards to employees who have worked there for 5 years, and 10 gift cards for employees working there for 10 years. He gives out a total of 282 gift cards.
He has 14 more employees that working there for 3 years, than for 5 years. Also there are 3 fewer employees who have been working there for 10 years than for 5 years.
How many employees have been working there for 10 years?

Answer by ikleyn(52788) (Show Source): You can put this solution on YOUR website!
.

3x + 5y + 10z = 282    (1)  (counting the cards)


where x, y and z are the corresponding numbers of employees.


Two additional equations, from the condition, are


x - 14 = y             (2)

y - 3 = z              (3)


Now you can express  y = z+3  from  (3),  and  x = y+14 = (z+3) + 14 = z + 17 from (2) and (3).  Substitute it into eq(1) to get


3*(z+17) + 5*(z+3) + 10z = 282.


Simplify and solve for z


3z + 51 + 5z + 15 + 10z = 282,

18z + 66 = 282,

18z = 282 - 66 = 216  ====>  z = 216/18 = 12.


ANSWER.  12 employees have been working there for 10 years.

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