Your test scores in one class are 83 and 89. What possible scores can you earn on your next test to have a test average between 86 and 90, inclusive? Your score on the third test must be between and inclusive. (Use ascending order.)

Answer 1

To calculate the average score, we sum all the scores and divide by the number of total tests. Let's call the score on the third test $x$.

The sum of the three scores is $83 + 89 + x$. The average is $\frac{83 + 89 + x}{3}$. To have an average between 86 and 90, inclusive, we need:

$$86 \leq \frac{83 + 89 + x}{3} \leq 90$$

Multiplying through by 3:

$$258 \leq 83 + 89 + x \leq 270$$

Adding $-83-89$ to all terms of the inequality:

$$86 \leq x \leq 98$$

So, the possible scores you can earn on your next test to have a test average between 86 and 90, inclusive, are in the range of $\boxed{86}$ to $\boxed{98}$.