First off, Happy 4th!
Let the lowest score be L, the highest score be H, and the sum of all other scores be S.
The average is found by taking a sum, and dividing it by the number of terms in the sum.
When we remove the low score and take the average, we only have 29 scores total:
(Sum of scores not including the low score)/(total number of scores minus the number of scores removed) = 8.5, or
(S + H)/29 = 8.5. Multiply both sides by 29:
S + H = 246.5
Using similar logic, when we remove the highest score, we have
(S + L)/29 = 8.2. Multiply both sides by 29:
S + L = 237.8
The range of the scores is found by subtracting the lowest score from the highest. Subtracting one equation from the other allows us to find the range:
S + H + 0 = 246.5
S + 0 + L = 237.8. Subtract the lower equation to get
0 + H - L = 8.7.
The answer is choice E.
