In drilling the world's deepest hole,it was found that the temperature $T$ in degrees Celsius,$x \text{ km}$ below the earth's surface,is given by $T = 30 + 25(x - 3)$,where $3 \leq x \leq 15$. At what depth will the temperature be between $155^{\circ}C$ and $205^{\circ}C$?

(N/A) Given the temperature formula: $T = 30 + 25(x - 3)$,for $3 \leq x \leq 15$.
We need to find the depth $x$ such that $155 < T < 205$.
Substituting the expression for $T$:
$155 < 30 + 25(x - 3) < 205$
Subtract $30$ from all parts:
$155 - 30 < 25(x - 3) < 205 - 30$
$125 < 25(x - 3) < 175$
Divide by $25$:
$5 < x - 3 < 7$
Add $3$ to all parts:
$5 + 3 < x < 7 + 3$
$8 < x < 10$
Thus,the temperature will be between $155^{\circ}C$ and $205^{\circ}C$ at a depth between $8 \text{ km}$ and $10 \text{ km}$.