First find a box you know for sure. This is kind of like sudoku if you’ve ever played that:
Under the total column we know that all those values MUST add up to 237
So X + 63 + 66 = 237
Or x = 108 (7th grade total)
Now let’s find another one that we can easily fill in.
Under neutral we know those values must add up to 45
So 17 + 8 + X =45
X = 20 (7th grade neutral)
Now with this information we can fill out 7th grade happy.
15 + 16 + 20 + X + 22 = 108
X = 35 (7th grade happy)
Now we can solve 6th grade happy
X + 35 + 25 = 79
Or x = 19 (6th grade happy)
Another easy one is unhappy total
9 + 16 + 12 = X
Or X = 37 (unhappy total)
Now let’s solve 6th grader very unhappy with new information we found
X + 9 + 17 + 19 + 12 = 63
Or x = 6 (6th grade very unhappy)
Using that we can find 8th grade very unhappy
6 + 15 + X = 31
Or x = 10 (8th grade very unhappy)
Now solve 8th grade very happy
10 + 12 + 8 + 25 + X = 66
Or x = 11 (8th grade very happy)
Now solve very happy total and that’s all
12 + 22 + 11 = X
X= 45 (very happy total)
Now to check our work do all the mood totals add up?
31 + 37 + 45 + 79 + 45 = 237 which checks out