Answer:
15?
Step-by-step explanation:
Scores are {72, 97, 82, x} where x is the unknown fourth score
They add up to 72+97+82+x = x+251
Divide this sum over four because there are four scores we want to average out. We end up with (x+251)/4 = M where M is the mean. Asa wants the mean to be 82, so make M = 82.
We can replace M with 82 and solve for x like so
(x+251)/4 = M
(x+251)/4 = 82
x+251 = 4*82
x+251 = 328
x = 328-251
x = 77
Asa needs a score of 77 on the fourth test so that the mean of the four tests is 82. If she scores higher than 77 on the fourth test, then the mean will be larger than 82.
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Depending on what your teacher is looking for, the first step is to establish your variable. So you would say "let x = fourth score". However, that seems too easy. So perhaps your teacher is looking for the equation (x+251)/4 = 82 or some variant of it.
To get the distance between
and 
, we subtract from
That is,
We change the mixed number to improper fraction now to get,
This is the same as,
We collect LCM to be 4
This gives us,
Convert back to mixed number to get,
Therefore the distance between the two numbers is
Note that the other way round will result in negative value. That is subtracting 6 from will give 
But since this is distance we find the absolute value and get the same result.
13.6g-22 Is the correct answer:)
