Your test scores in one class are 85 and 88. What possible scores can you earn on your nest test to have a test average between 86 and 90, inclusive?
x+=-5
85
To find the possible scores on your next test, we first need to determine the range of averages that will fall between 86 and 90 inclusive.
The average of your test scores can be calculated by summing up all the test scores and dividing it by the number of tests taken. In this case, you have two previous test scores, which we can denote as Test1 and Test2.
So, the average of your test scores can be represented as:
Average = (Test1 + Test2 + NextTest) / 3
To have an average between 86 and 90 inclusive, we can set up the following inequality:
86 ≤ Average ≤ 90
Substituting the average formula, we get:
86 ≤ (Test1 + Test2 + NextTest) / 3 ≤ 90
Multiplying the inequality by 3 to eliminate the fraction, we get:
258 ≤ Test1 + Test2 + NextTest ≤ 270
Now, to find the possible scores for your next test, we need to subtract the sum of your previous test scores from both ends of the inequality:
258 - (Test1 + Test2) ≤ NextTest ≤ 270 - (Test1 + Test2)
Substituting the given test scores (85 and 88), we get:
258 - (85 + 88) ≤ NextTest ≤ 270 - (85 + 88)
Simplifying, we have:
258 - 173 ≤ NextTest ≤ 270 - 173
85 ≤ NextTest ≤ 97
Therefore, the possible scores you can earn on your next test to have a test average between 86 and 90, inclusive, are any scores between 85 and 97, inclusive.