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

There were originally 10 friends in the group.

Step-by-step explanation:

Let's assume that there were initially x friends in the group. So, the total cost of the trip was $800 and each friend would have paid $800/x before two friends decided not to go. After two friends decided not to go, the remaining friends still divided the $800 cost equally, but each friend's share increased by $20. Therefore, the amount each friend paid after is $800/x-2.

We can set up an equation: $800/x - $800/x-2 = $20.

Simplifying the equation, we get $800(x-2) - $800(x) = $20(x)(x-2). Solving this equation, we find that x = 10.

Therefore, there were originally 10 friends in the group.

Answer 2

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

`(800)/(x-2) - (800)/(x) =20`
Divide through by 20.

`(40)/(x-2) - (40)/(x) =1\\ \\(40x-40(x-2))/(x(x-2)) =1 \\ \\ (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.