Final answer:
Tony needs to score 88 points on his fifth test to achieve an average score of 78 across all five tests.
Step-by-step explanation:
The student needs to find out what score is necessary on the fifth test to achieve an average score of 78. We start by calculating the total points needed for five tests to get an average of 78.
Total points needed = average × number of tests = 78 × 5 = 390 points.
Next, we add the scores of the four tests the student has already taken: 98 + 66 + 74 + 64 = 302 points. We subtract the sum of these scores from the total points needed to find out what the student needs to score on the fifth test.
Score needed on the fifth test = Total points needed - Points already scored = 390 - 302 = 88 points.
Therefore, Tony needs to score 88 points on his fifth test to have an average of 78.