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