Your test scores in one class are 81 and 87. What possible scores can you earn on your next test to have a test average between 84 and 99, inclusive?

Answer 1

Let us assume that the score of the next test will be denoted as $x.$ We are given that $\frac{81+87+x}{3}\geq84,$ which when simplified gives $200\geq x.$ We are also given that $\frac{81+87+x}{3}\leq99,$ which when simplified gives $x\leq123.$ Thus, all values of $x$ from $\boxed{200}$ to $\boxed{123}$ (inclusive) will give us a test average between 84 and 99.