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

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) (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?
---------------
Let original # of contributers be "x".
Original aver cost per person is 100/x
-----
After 2 dropped out the # is "x-2"
New aver cost is 100/(x-2)
----
Equation:
New aver - Old aver = 2.50
100/(x-2) - (100)/x = 2.50
------
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
---
Positive solution:
x = 10 (original number of co-workers)
x-2 = 8 (# of workers who contributed to the present)
===================================
Cheers,
Stan H.
=========
RELATED QUESTIONS
Bob, Celia, Sam, and Daniel contributed money to buy their boss a retirement gift. Sam... (answered by josgarithmetic)

Bob, Celia, and Daniel contributed money to buy their boss a retirement gift. Sam and... (answered by ikleyn)

i have a word problem which i cannot find a formula for it? the problem goes like this... (answered by scott8148)

The amount of money that each person must contribute to buy a retirement gift for a... (answered by Boreal)

To calculate a colleague's graduation, the m workers in an office agreed to contribute... (answered by ptaylor)

To celebrate a colleague's graduation, the "m" workers in an office agreed to contribute... (answered by ccs2011)

A group of 3 workers need 20 days to do a certain job. How long would it take a group of (answered by josgarithmetic)

A group of 3 workers need 20 days to do a certain job. How long would it take a group of... (answered by josgarithmetic)

A group of students agreed that each would chip in the same amount to pay for a party... (answered by solver91311)