A group of friends decide to buy a vacation home for $120,000, sharing the cost equally. If they can find one more person to join them, each person's

Question

group of friends buy vacation home for $120,000. If one more person is added, the amount of money equally shared by the group will decrease by $6,000. How many people are originally in the group??

Answer 1

I would set this up as two equations:

c = original cost per person

x = original number of people

 

so:

cx=120000

(c-6000)(x+1) = 120000

 

Solve the first equation for c and substitute in the second equation.

 

Once you do all the math and simplify, you will end up with a quadratic:

x² + x - 20 = 0

(x-4)(x+5) = 0

so x = 4, -5

 

Have to eliminate -5 (there cannot be -5 people), so the answer is there were 4 people originally in the group.

 

To check this: 120,000/4 = 30,000.

Further: 120,000/5 = 24,000 which is a decrease per person of 6,000.