Answer
$8$ people
Work Step by Step
Step 1. Assume there were $x$ number of winners in the original group; then each person should receive $\frac{20000000}{x}$ dollars.
Step 2. Adding two more winners, we have $x+2$ winners and each should receive $\frac{20000000}{x+2}$ dollars.
Step 3. Based on the condition given, we have $\frac{20000000}{x}-\frac{20000000}{x+2}=500000$, which can be simplified to $\frac{40}{x}-\frac{40}{x+2}=1$
Step 4. Multiply $x(x+2)$ on both sides; we have $40(x+2)-40x=x(x+2)$ or $x^2+2x-80=0$, which can be factored as $(x-8)(x+10)=0$
Step 5. Discard the negative solution; we have $x=8$
