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 - Mathematics

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Sum

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.

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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.

Concept: Inequalities - Introduction
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APPEARS IN

NCERT Mathematics Exemplar Class 11
Chapter 6 Linear Inequalities
Exercise | Q 8 | Page 107
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