Question 7
In a Mathematics contest, the scores of $10$ students, which are all positive integers, are shown in the table below, except for Grace’s score.
| Student | Score |
|---|---:|
| Alice | 23 |
| Bob | 6 |
| Carla | 14 |
| David | 13 |
| Eric | 23 |
| Freya | 9 |
| Grace | ? |
| Helen | 12 |
| Ivory | 29 |
| Jordan | 19 |
The committee remembers that the difference between the average of the six highest scores and the average of the six lowest scores is $12$. What is the sum of all the possible scores of Grace?
| Student | Score |
|---|---:|
| Alice | 23 |
| Bob | 6 |
| Carla | 14 |
| David | 13 |
| Eric | 23 |
| Freya | 9 |
| Grace | ? |
| Helen | 12 |
| Ivory | 29 |
| Jordan | 19 |
The committee remembers that the difference between the average of the six highest scores and the average of the six lowest scores is $12$. What is the sum of all the possible scores of Grace?