Question

A group of winning ticket holders share equally in a $30,000,000 lottery. Before the money is divided, one more winning ticket holder is declared. As a result , each person's share is reduced by $1,000,000. How many people were in the orginal group of winners?

Answer 1

30 people as if you divide 30,000,000 by 1,000,000 it gets 30

Answer 2

Answer: The number of people in the original group of winners is 5.

Explanation:

Let the number of people in the original group of winners be 'x'.

Amount of lottery = $30,000,000

if the number of people is increased by 1 means that x+1.

So, each person's share is reduced by $1,000,000.

According to question, it becomes,

`(30000000)/(x)-(30000000)/(x+1)=1000000\\\\(30)/(x)-(30)/(x+1)=1\\\\30((x+1-x)/(x^2+x))=1\\\\(1)/(x^2+x)=(1)/(30)\\\\30=x^2+x\\\\x^2+x-30=0\\\\x^2+6x-5x-30=0\\\\x(x+6)-5(x+6)=0\\\\(x+6)(x-5)=0\\\\x=-6,5`

we discard the negative value of x i.e. -6.

So, the number of people in the original group of winners is 5.