x = score on the last test (fifth test)
To obtain the average, we add up the values and divide by 5 (as there are 5 tests). We want this average to be 80 so we can figure out x
(81+78+84+75+x)/5 = 80
Solve for x
(81+78+84+75+x)/5 = 80
(318+x)/5 = 80
318+x = 80*5
318+x = 400
x+318 = 400
x = 400-318
x = 82
The lowest score Alexandria can get is 82, so her average is 80. Any higher score on the fifth test leads to the average being larger than 80.
Answer: 82
As a check, you can add up the five scores (81, 78, 84, 75, and the new score 82 we just found) and then divide that sum over 5. You should get 80 as a result.
