The water acidity in a pool is considered normal when the average pH reading of three daily measurements is between $8.2$ and $8.5$. If the first two pH readings are $8.48$ and $8.35$,then find the range of $pH$ value for the third reading that will result in the acidity level being normal.

(N/A) Let the third pH reading be $x$.
The average of the three readings must be between $8.2$ and $8.5$.
$\therefore 8.2 < \frac{8.48 + 8.35 + x}{3} < 8.5$
Multiply the entire inequality by $3$:
$\therefore 3 \times 8.2 < 16.83 + x < 8.5 \times 3$
$\therefore 24.6 < 16.83 + x < 25.5$
Subtract $16.83$ from all parts:
$\therefore 24.6 - 16.83 < x < 25.5 - 16.83$
$\therefore 7.77 < x < 8.67$
Hence,the third pH reading must be in the range $(7.77, 8.67)$.