Your test Scores in one class are 77 and 85. What possible scores can you earn on your best test to have a test average between 81 and 87 inclusive

Answer 1

Right now, you have an 81 test average: (77+85)/2 = 162/2 = 81. Your next test has to be at least 81 to avoid having the average drop below 81.

77+85 + x = 162+x

your new average after one more test will be (162+x)/3 = 54+ x/3. If you want an 87 average or less, you can't get more than x where 54+x/3 is less than or equal to 87

54+x/3 = 87

x/3 = 87-54 = 33

x = 33(3) = 99

If you get 100, your average will go above 87, slightly.

to stay in the 81 to 87 range, you need another test score of 81 to 99.

77+85+99 = 261. 261/3 = 87

77+85+ 81 = 243. 243/3 = 81

Any test score lower than 81 or higher than 99 puts you outside the 81 to 87 test average.