Explanation:

- You have a set of fifteen numbers with an average of 12.

- The sum of all these numbers is 15 multiplied by 12, which is 180.

- If you add 7 to each number, the total increase in the sum is 15 times 7, which is 105.

- The new sum is 180 plus 105, equaling 285.

- The new average is 285 divided by 15, which equals 19.

- Option 1 (84): Incorrect, as the calculated new average is not 84.

- Option 2 (105): Incorrect, this isn't the average but the total increase.

- Option 3 (19): Correct, as the new average is 19.

- Option 4 (22): Incorrect, as this does not match the calculated new average.