Hey there! I'm happy to help!
We have 5 numbers that will give us an average score of 80.
75,82,71,84,x
What we do is add these all up and divide by 5 to get 80. Let's go backwards to find x.
We multiply by 5.
80(5)=400
We subtract all of the numbers except for x.
400-75-82-71-84=88
Therefore, the score on the next test has to be 88 to have the student's average be 80.
Have a wonderful day! :D