How many people are in the group

Question

A group of people would like to buy a vacation cabin for $600,000, sharing the cost equally. If they could find five more people to join them, each person's share would be reduced by $6,000. How many people are in the group 

Answer 1

x=# of people in the group

600,000/x=600,000/(x+5)+6000

multiply both sides by the LCM which is (x)(x+5)

600,000(x+5)=600,000x+6000(x²)+6000(5x)

600,000x+3,000,000=600,000x+6000x²+30,000x

subtract 600,000x from both sides

3,000,000=6000x²+30,000x

6000x²+30,000x-3,000,000=0

divide both sides all terms by 6000

x²+5x-500=0

factor

500=5*2*2*5*5=(5*2*2)*(5*5) and 25-20=5, the coefficient of the middle term

(x+25)(x-20)=0

x-20=0

x=20 people are in the group (answer)

600,000/20=30,000

600,000/25=24,000

30,000-24,000=6000 less