Your test scores in one class are 78 and 84. What possible scores can you earn on your next test to have a test average between 81 and 87?

Any score between 81 and 99

Step-by-step explanation:

let the possible score be X

since we are given a range for the average between 81 and 87, our answer will also be a range which gives the lowest average score of 81 and the highest average score of 87.

Recall that average = sum of scores / number of scores.

In this case, number of scores is 3,

Hence

Average Score = (78 + 84 + X) / 3

Average Score = (162 + X) / 3 (multiply both sides by 3)

3 * (Average Score) = (162 + X) (subtract 162 from both sides)

X = 3 (Average Score) - 162

For the average score range of 81 to 87,

for average score = 81, X = 3 (81) - 162 = 81

for average score = 87, X = 3 (87) - 162 = 99

hence 81 < X < 99