She would have to score at least a 97% on her next math test.
Mean = 88 + 94 + 82 + 89 + 97 = 450
450/5 = 90
You could have found this answer without using trial and error.
If she wants to get a mean of 90 and she will have 5 tests, you can multiply these together.
This equals 450.
Now you need to find the minimum score she needs to get. Take 450 and subtract what the original 4 numbers equal, 353.
This gives you 97.
I hope that makes sense :)