\[T\text{ }=\text{ }30\text{ }+\text{ }25\left( x\text{ }\text{ }3 \right),\text{ }3\text{ }\le \text{ }x\text{ }\le \text{ }15;\]

where, T = temperature and x = depth inside the earth

The Temperature should be between 155°C and 205°C,

So, we get,

\[\begin{array}{*{35}{l}}

\Rightarrow ~155\text{ }<\text{ }T\text{ }<\text{ }205  \\

\Rightarrow ~155\text{ }<\text{ }30\text{ }+\text{ }25\left( x\text{ }\text{ }-3 \right)\text{ }<\text{ }205  \\

\Rightarrow ~155\text{ }<\text{ }30\text{ }+\text{ }25x\text{ }\text{ }-75\text{ }<\text{ }205  \\

\Rightarrow ~155\text{ }<\text{ }25x\text{ }\text{ }-45\text{ }<\text{ }205  \\

\end{array}\]

Adding 45 to each term, we get

\[\Rightarrow ~200\text{ }<\text{ }25x\text{ }<\text{ }250\]

Dividing each term by 25, we get

\[\Rightarrow ~8\text{ }<\text{ }x\text{ }<\text{ }10\]

Hence, temperature varies from 155° C to 205° C at a depth of 8 km to 10 km.