30 people as if you divide 30,000,000 by 1,000,000 it gets 30
Answer: The number of people in the original group of winners is 5.
Step-by-step 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,
[tex]\dfrac{30000000}{x}-\dfrac{30000000}{x+1}=1000000\\\\\dfrac{30}{x}-\dfrac{30}{x+1}=1\\\\30(\dfrac{x+1-x}{x^2+x})=1\\\\\dfrac{1}{x^2+x}=\dfrac{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[/tex]
we discard the negative value of x i.e. -6.
So, the number of people in the original group of winners is 5.
