Problem B

Letâ€™s Divvy These Up

At Yore Elementary School, each class has between \(15\) and \(35\) students. If there are \(78\) students in Grade \(6\), and all Grade \(6\) classes have the same number of students, how many Grade \(6\) classes are there?

At Hyz Elementary School, there is the same number of Grade \(6\) classes as at Yore, but there are \(84\) Grade \(6\) students. If all Grade \(6\) classes have the same number of students, how many students are in each Grade \(6\) class?

For each of the numbers in the first column of the table given below, first determine if it could be the total number of students in three very large classes of equal size, and then calculate the digit sum of the number. Do you notice any connection between these two things?

Note: The*digit sum*of a number is the sum of its digits. For example, the digit sum of \(63\) is \(6+3=9\).Number Could be total? Digit Sum \(1008\) \(1023\) \(1741\) \(2238\) \(1759\) \(1902\)

**Theme:** Number Sense