In a cinema, the price is 12 SF per person. Students however do only pay 9 SF, and children pay only 1 SF each. If the total amount paid by 41 persons is 400 SF, how many of them were students and how many children?
Solve this problem, discuss the method, and explain wether or not your method can be applied to the general problem where the prices are a, b, c, and the total amount paid by the n persons is m. How does the choice of a, b, c, n, m affect the number of solutions?
Erich Prisner, September 2003