We can solve this by first rewriting the demand functions as inverse demand functions (price in terms of quantity). For the group of 20 consumers, this is P = 20 - Q and for the group of 5, P = 9 - 0.5Q. We can now add up each individual's inverse demand function to create a societal inverse demand function. In this case we get P = 10 (20 - Q) + 5 (9- 0.5Q) = 200 - 10Q + 45 - 2.5Q = 245 - 12.5Q. Since we know that in a competitive market marginal cost equals price, we can set P to be 10. This yields the equation 10 = 245 - 12.5Q. Solving for Q set get 18.8. Therefore the socially optimal number of streetlights is between 18 and 19.