There are 30 (not necessarily distinct) real numbers written on a board. We know that no matter how we divide these numbers into 10 groups of size 3, there would be at least 2 groups with equal sums. Find the maximum number of distinct numbers on the board.

Mason and christian go to the movie theater and purchase refreshments for their friends. mason spends a total of $45.75 on 3 bags of popcorn and 6 drinks. christian spends a total of $71.50 on 6 bags of popcorn and 4 drinks. write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink. using these equations, determine and state the price of a drink, to the nearest cent.