Answer
$9.6$
Work Step by Step
Let $x$ be the final score.
The given conditions translate to
\begin{array}{l}\require{cancel}
\dfrac{9.5+9.7+9.9+9.7+9.7+9.6+9.5+x}{8}\ge9.65
.\end{array}
Using the properties of inequality, then
\begin{array}{l}\require{cancel}
\dfrac{67.6+x}{8}\ge9.65
\\\\
8\cdot\dfrac{67.6+x}{8}\ge8\cdot9.65
\\\\
67.6+x\ge77.2
\\\\
x\ge77.2-67.6
\\\\
x\ge9.6
.\end{array}
Hence, the minimum score to win the silver medal is $
9.6
.$
