Question 9
The following (incomplete) table records the numbers of students with a given number of marbles:
| $c$ | 0 | 1 | 2 | 3 | … | 13 | 14 | 15 |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Number of students with $c$ marbles | 9 | 5 | 7 | 23 | … | 5 | 2 | 1 |
In addition, we also know the following:
- The maximum number of marbles that a student has is $15$.
- The students with $3$ or more marbles have an average of $6$ marbles.
- The students with $12$ or fewer marbles have an average of $5$ marbles.
What is the total number of marbles combined across all the students?
| $c$ | 0 | 1 | 2 | 3 | … | 13 | 14 | 15 |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Number of students with $c$ marbles | 9 | 5 | 7 | 23 | … | 5 | 2 | 1 |
In addition, we also know the following:
- The maximum number of marbles that a student has is $15$.
- The students with $3$ or more marbles have an average of $6$ marbles.
- The students with $12$ or fewer marbles have an average of $5$ marbles.
What is the total number of marbles combined across all the students?