I am going to teach some grade 9 students about solving linear and quadratic equations. I am looking for a question from every day life (of a teenager) or a puzzle which is hard to solve without using algebra. There are of course loads out there in textbooks and the internet, but I haven't yet found one which is really intriguing and which could arouse the interest even of a student who has other things on his/her mind and who has a general dislike for school-mathematics.
For example questions concerning the respective speeds, distances and time-periods of two vehicles with respect to each other are classic examples motivating linear equations, but they don't really seem to be relevant for real life (from the perspective of a teenager) nor are they particularly fascinating (at least for someone who isn't interested in mathematics anyway).
I'd like to begin the subject with such a question and let the students work on it together for maybe half an hour or so (i.e. the question shouldn't be too easy to solve); hopefully this way they will see themselves how useful it can be to introduce variables.