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(52903)   (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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