Answer
$10$ people.
Work Step by Step
Step 1. Assume $x$ number of people originally intended to go; the original cost would be $\frac{1500}{x}$
Step 2. With 4 people changing their minds, we have $x-4$ left and the cost would be $\frac{1500}{x-4}$
Step 3. Since $\frac{1500}{x-4}-\frac{1500}{x}=100$, multiply both sides by $x(x-4)$. We have $1500x-1500x+6000=100x(x-4)$ or $x^2-4x-60=0$
Step 4. Factor the above equation to get $(x+6)(x-10)=0$, and choose the positive solution to get $x=10$ people.
