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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?

Respuesta :

jepessoa

Answer:

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.

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