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Question
The water acidity in a pool is considerd 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, find the range of pH value for the third reading that will result in the acidity level being normal.
Solution
Let the third pH value be x.
Given that first pH value = 8.48
And second pH value = 8.35
∴ Average value of pH = `(8.48 + 8.35 + x)/3`
But average value of pH lies between 8.2 and 8.5
∴ `8.2 < (8.48 + 8.35 + x)/x < 8.5`
⇒ 24.6 < 16.83 + x < 25.5
⇒ 24.6 – 16.83 < x < 25.5 – 16.83
⇒ 7.77 < x < 8.67
Hence, the third pH value lies between 7.77 and 8.67.
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