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 is 7.48 and 7.85, find the range of pH value for the third reading that will result in the acidity level is normal.
pH value of the first reading = 7.48
pH value of the second reading = 7.85
We need to find the range of the pH value for the third reading so that the acidity level in the pool is normal.
But the acidity level in the pool is considered normal when the average pH reading of the three measurements is between 7.2 and 7.8.
That is, 7.2 < average pH reading of the three measurements < 7.8 …(i)
Let us find the average pH reading of the three measurements.
For this, let the pH value of the third reading be x.
Then, the average is given by
Substituting this value of average in inequality (i), we get
Multiply 3 throughout the inequality, we have
⇒ 22.6 < 15.33 + x < 23.4
Now, subtract 15.33 throughout the inequality,
⇒ 22.6 – 15.33 < 15.33 + x – 15.33 < 23.4 – 15.33
⇒ 7.27 < x < 8.07
This means, x lies between values 7.27 and 8.07.
Thus, the pool’s acidity level would be normal when the range of pH value in the third measurement would be between 7.27 and 8.07.