Algebra 1

85$\leq$x$\leq$100
Let call x the next test score the person have to get in order to have average between 85 and 90 inclusively. 85$\leq$$\frac{83+87+x}{3} \leq90 => 85\leq$$\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