A student's average ( arithmetic mean) test score on 4 tests is 78. What must be the students score on a 5th test for the students average score on the 5th test to be 80?

Let xx be the score the student needs on the 5th test.

The average score after 5 tests is 8080.

So, the total of all 5 test scores will be 80×5=40080×5=400.

The total of the first 4 test scores is 78×4=31278×4=312.

To find the score needed on the 5th test, subtract the total of the first 4 tests from the desired total:

400−312=88400−312=88

So, the student needs to score 88 on the 5th test to achieve an average score of 80.