investors in a start - up will share $3,000 in dividends evenly. if 50 more investors are added, the…

Explanation:

Step1: Multiply through by $x(x + 50)$

$3000(x + 50)-3x(x + 50)=3000x$

Step2: Expand the expressions

$3000x+150000-3x^{2}-150x = 3000x$

Step3: Simplify the equation

$-3x^{2}-150x + 150000=0$ Divide by - 3: $x^{2}+50x - 50000=0$

Step4: Solve the quadratic equation

Using the quadratic formula $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$ for $ax^{2}+bx + c = 0$. Here $a = 1$, $b = 50$, $c=-50000$. First, calculate the discriminant $\Delta=b^{2}-4ac=(50)^{2}-4\times1\times(-50000)=2500 + 200000=202500$. Then $x=\frac{-50\pm\sqrt{202500}}{2}=\frac{-50\pm450}{2}$. We get two solutions: $x_1=\frac{-50 + 450}{2}=\frac{400}{2}=200$ and $x_2=\frac{-50-450}{2}=\frac{-500}{2}=-250$. Since the number of investors cannot be negative, we discard $x_2$.

Answer:

200