s=(70-x)(3000+ 100x)=- 100x^2+4000x+2 10000

Then x=20 can be obtained by the maximum or derivative of the quadratic function.

If you choose to fill in the blanks, you can do this:

When the fare is 100, the number of people is zero and the income is zero. When the fare drops to 0, the income is also 0, so the optimal value is the median value of 50 (this is the symmetry of quadratic function).