your test scores in one class are 80 and 88. what possible scores can you earn on your next test to have a test average between 84 and 89, inclusive?
well, try 84
(80 + 88 + x)/3 = 84
168/3 + x/3 = 84
168 + x = 252
x = 84 of course since that was original average
now 89
80 + 88 + x = 3*89 = 267
168 + x = 267
x = 99
so
84 </= x </= 99
To find the range of possible scores on your next test, you need to consider the desired test average range of 84 to 89, inclusive.
To calculate the average, you add up all the test scores and divide by the number of tests. Since you have two test scores so far, you can find the desired average within the given range by using the equation:
Average = (Sum of test scores + Score on next test) / (Number of tests + 1)
Let's solve this equation with the lower bound of the desired average range (84) first:
84 = (80 + 88 + Score on next test) / 3
Now, simplify the equation:
252 = 168 + Score on next test
Score on next test = 252 - 168
Score on next test = 84
Therefore, for the lower bound of the desired average range (84), you need to score at least an 84 on your next test.
Next, let's solve the equation for the upper bound of the desired average range (89):
89 = (80 + 88 + Score on next test) / 3
Again, simplify the equation:
267 = 168 + Score on next test
Score on next test = 267 - 168
Score on next test = 99
Therefore, for the upper bound of the desired average range (89), you can score up to 99 on your next test.
In summary, the possible scores you can earn on your next test to have a test average between 84 and 89, inclusive, are any score from 84 to 99.