Question 158
The table below shows some of the results of the last Pirajuba Fishing Festival, showing how many competitors $q$ caught $n$ fish for some values of $n$.
| $n$ | 0 | 1 | 2 | 3 | $\ldots$ | 13 | 14 | 15 |
| :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |
| $q$ | 9 | 5 | 7 | 23 | $\ldots$ | 5 | 2 | 1 |
The news published in the town newspaper reported that:
i) the winner caught 15 fish;
ii) among those who caught 3 or more fish, the average was 6 fish caught; and
iii) among those who caught 12 or fewer fish, the average number of fish caught was 5.
a) What was the total number of fish caught during the festival?
b) How many competitors caught from 4 to 12 fish?
| $n$ | 0 | 1 | 2 | 3 | $\ldots$ | 13 | 14 | 15 |
| :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |
| $q$ | 9 | 5 | 7 | 23 | $\ldots$ | 5 | 2 | 1 |
The news published in the town newspaper reported that:
i) the winner caught 15 fish;
ii) among those who caught 3 or more fish, the average was 6 fish caught; and
iii) among those who caught 12 or fewer fish, the average number of fish caught was 5.
a) What was the total number of fish caught during the festival?
b) How many competitors caught from 4 to 12 fish?