The water acidity in a pool is considered normal when the average pH reading of three daily measurements is between 7.2 and 7.8.
Question:
The water acidity in a pool is considered normal when the average pH reading of three daily measurements is between 7.2 and 7.8. If the first two pH reading are 7.48 and 7.85, find the range of pH value for the third reading that will result in the acidity level being normal
Solution:
Let x be the third pH value.
Then, $7.2<\frac{7.48+7.85+x}{3}<7.8$
$\Rightarrow 7.2<\frac{15.33+x}{3}<7.8$
$\Rightarrow 21.6<15.33+x<23.4 \quad$ (Multiplying throughout by 3 )
$\Rightarrow 21.6-15.33<15.33+x-x<23.4-15.33$
$\Rightarrow 6.27
Hence, the range for the $\mathrm{pH}$ value for the third reading must be between $6.27$ and $8.07$