Before taking her final test, Tammys mean was 88% If she scores 68% on the final, her mean will be 86%. However, if she scores 98% on the final test, her mean will be 89%. How many test will Teresa takes in total.
To solve this problem, we can use the concept of weighted averages.
Let's assume that Tammy has taken "x" tests before her final test.
We are given three scenarios:
1. Before the final test, Tammy's mean is 88%. This means that the sum of her scores before the final test is 88x.
2. If she scores 68% on the final test, her mean will be 86%. This means that the sum of her scores after taking the final test would be (88x + 68) and the number of tests she has taken would be (x + 1).
3. If she scores 98% on the final test, her mean will be 89%. This means that the sum of her scores after taking the final test would be (88x + 98) and the number of tests she has taken would be (x + 1).
Now, we can form two equations based on the second and third scenarios:
(88x + 68) / (x + 1) = 86
(88x + 98) / (x + 1) = 89
To solve these equations, we can cross-multiply and simplify:
88x + 68 = 86x + 86
88x + 98 = 89x + 89
Solving these equations, we find:
2x = 18
x = 9
Therefore, Tammy has taken a total of 9 + 1 = 10 tests. She will take 10 tests in total.