Going into the final exam, which will count as two tests, Brandi has test scores of 75, 86, 70, 61, and 96. What score does Brandi need on the final in order to have an average score of 80?

Step 1: Find the total possible points before the final exam:
Total possible points = 5 tests * 100 points = 500 points

Step 2: Find the total points earned before the final exam:
Total points earned = 75 + 86 + 70 + 61 + 96 = 388 points

Step 3: Let x be the score Brandi needs on the final exam. Since the final exam will count as two tests, the total points earned after the final exam will be:
388 + x

Step 4: The average score with the final exam included will be:
\frac{388+x}{7}=80

Step 5: Solve for x:
388+x=7*80
388+x=560
x=560-388
x=172


Answer: Brandi needs to score 172 on the final exam in order to have an average score of 80.