Answer
85$\leq$x$\leq$100
Work Step by Step
Let call x the next test score the person have to get in order to have average between 85 and 90 inclusively.
85$\leq$$\frac{83+87+x}{3}$ $\leq$90
=> 85$\leq$$\frac{83+87+x}{3}$ and $\frac{83+87+x}{3}$$\leq$90
=>255$\leq$83+87+x and 83+87+x$\leq$270
=>255$\leq$170+x and 170+x$\leq$270
=>80$\leq$x and x$\leq$100
=> 80$\leq$x$\leq$100
