Question

A group of friends decided to divide the $800 cost of a trip equally among themselves. when two of the friends decided not to go on the trip, those remaining still divided the $800 cost equally, but each friendâs share of the cost increased by $20. how many friends were in the group originally?

Answer 1

Total cost for the trip = $800.

Let x  =  original number of friends.
Therefore the equally shared cost of the trip for each friend is $800/x.

After 2 friends drop out, the cost for each friend increases to $800/(x-2).
The increase in cost for each remaining friend is $20, therefore
$\frac{800}{x-2} - \frac{800}{x} =20$
Divide through by 20.
$\frac{40}{x-2} - \frac{40}{x} =1\\ \\\frac{40x-40(x-2)}{x(x-2)} =1 \\ \\ \frac{80}{x(x-2)} =1$
Cross multiply.
x(x - 2) = 80
x² - 2x - 80 = 0
(x + 8)(x - 10) = 0
x = -8 or 10
Reject x = -8 because we cannot have a negative number for friends.
x = 10

Answer: There were 10 friends in the original group.