SOLUTION: A group of co-workers agreed that each would contribute the same amount to buy their boss a $100 birthday gift. At the last minute, 2 of the people decided not to chip in. This inc

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Question 411911: A group of co-workers agreed that each would contribute the same amount to buy their boss a $100 birthday gift. At the last minute, 2 of the people decided not to chip in. This increased the amount that the remaining had to contribute by $2.50 per person. How many people actually contributed to the gift?
y=(x-2)+2.50(100)
y=x-2+250
y=x+248
y-248=x
y=(y-248-2)+250
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A group of co-workers agreed that each would contribute the same amount to buy their boss a $100 birthday gift. At the last minute, 2 of the people decided not to chip in. This increased the amount that the remaining had to contribute by $2.50 per person. How many people actually contributed to the gift?
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Let original # of contributers be "x".
Original aver cost per person is 100/x
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After 2 dropped out the # is "x-2"
New aver cost is 100/(x-2)
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Equation:
New aver - Old aver = 2.50
100/(x-2) - (100)/x = 2.50
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100x -100(x-2) = 2.5x(x-2)
200 = 2.5x^2-5x
2.5x^2-5x-200 = 0
25x^2-50x-2000 = 0
x^2 - 2x- 80 = 0
(x-10)(x+8) = 0
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Positive solution:
x = 10 (original number of co-workers)
x-2 = 8 (# of workers who contributed to the present)
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Cheers,
Stan H.
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