A group of friends decides to buy a vacation home for $360,000, sharing the cost equally. If they can find one more person to join them, each person's contribution will drop by $4000. How many people are in the group?

9 friends

Explanation:

The group is made up of F number of friends, so the current cost per friend is 360000/F.

If one more friend is included in the purchase, the cost per friend will be: 360,000 / (F + 1)

360,000 / (F + 1) = 360,000/F - 4,000

360,000/F - 360,000 / (F + 1) = 4,000

360,000 (1/F - 1 / (F + 1) = 4,000

90 (1/F - 1 / (F + 1) = 1

90 [ (F + 1) - F] / [F (F + 1) ] = 1

90 (F + 1 - F) / [F (F + 1) ] = 1

90 { 1 / [F (F + 1) ]} = 1

90 / [F (F + 1) ] = 1

90 = F (F + 1)

90 = F² + F

F² + F - 90 = 0

(F + 10) (F - 9) = 0

F = - 10 or 9

Since people cannot be negative, then the total number of friends is 9.