Alula has the following quiz scores: 17, 10, 9, 14, 16, 8 and 10. What must the sum of her next three quiz scores be in order to have an overall average of 14?
Alula has already taken 7 quizzes, so after taking three more quizzes she will have 10 scores.  For these scores to have an average of 14, they must have a sum of $14\times10=140$.  The sum of 17, 10, 9, 14, 16, 8, and 10 is 84, so the three remaining scores must sum to $140-84=\boxed{56}$.