Math Help - Math puzzle

After a math lecture in Harvard the students went to the cafeteria and each one of them took a cup of tea and cheese sandwich. They all paid $18.94. How many students where they?

Originally Posted by karimwahab

After a math lecture in Harvard the students went to the cafeteria and each one of them took a cup of tea and cheese sandwich. They all paid $18.94. How many students where they?

There is insufficient information to give a unique answer.

Originally Posted by karimwahab

After a math lecture in Harvard the students went to the cafeteria and each one of them took a cup of tea and cheese sandwich. They all paid $18.94. How many students where they?

As stated here, there is no plausible solution. In fact, 1894 = 2×947, both of which factors are prime. So either there were 2 students and the cafeteria was ripping them off, or there were 947 students and the cafeteria is heavily subsidised.

In fact, I believe that the total payment should be $18.49. In that case, 1849 = 43^2. That gives a unique solution: 43 students, each paying 43¢. That's pretty good value for tea and a sandwich. I guess the cafeteria is subsidised after all.

Unless this is a trick question in which the solution is to look up Harvard policies to see what their maximum class size is! Or what the seating configuration is in their Mathematics lecture halls.

Originally Posted by Opalg

As stated here, there is no plausible solution. In fact, 1894 = 2×947, both of which factors are prime. So either there were 2 students and the cafeteria was ripping them off, or there were 947 students and the cafeteria is heavily subsidised.

In fact, I believe that the total payment should be $18.49. In that case, 1849 = 43^2. That gives a unique solution: 43 students, each paying 43¢. That's pretty good value for tea and a sandwich. I guess the cafeteria is subsidised after all.

But did each student pay the same amount?

Originally Posted by Yendor

But did each student pay the same amount?

Why wouldn't they?