Advertisements
Advertisements
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.
Advertisements
Solution
Let x be the third pH value.
\[\text{ Then }, 7 . 2 < \frac{7 . 48 + 7 . 85 + x}{3} < 7 . 8\]
\[ \Rightarrow 7 . 2 < \frac{15 . 33 + x}{3} < 7 . 8\]
\[ \Rightarrow 21 . 6 < 15 . 33 + x < 23 . 4 \left( \text{ Multiplying throughout by } 3 \right)\]
\[ \Rightarrow 21 . 6 - 15 . 33 < 15 . 33 + x - x < 23 . 4 - 15 . 33\]
\[ \Rightarrow 6 . 27 < x < 8 . 07\]
\[\text{ Hence, the range for the pH value for the third reading must be between } 6 . 27 \text{ and } 8 . 07\]
APPEARS IN
RELATED QUESTIONS
Solve the following system of inequalities graphically: 3x + 2y ≤ 12, x ≥ 1, y ≥ 2
Solve the following system of inequalities graphically: x + y≥ 4, 2x – y > 0
Solve the following system of inequalities graphically: 2x – y > 1, x – 2y < –1
Solve the following system of inequalities graphically: 2x + y≥ 8, x + 2y ≥ 10
Solve the following system of inequalities graphically: x + y ≤ 9, y > x, x ≥ 0
Solve the following system of inequalities graphically: 3x + 4y ≤ 60, x + 3y ≤ 30, x ≥ 0, y ≥ 0
Solve the following system of inequalities graphically: x – 2y ≤ 3, 3x + 4y ≥ 12, x ≥ 0, y ≥ 1
Solve the following system of inequalities graphically: 4x + 3y ≤ 60, y ≥ 2x, x ≥ 3, x, y ≥ 0
Solve the following system of inequalities graphically: 3x + 2y ≤ 150, x + 4y ≤ 80, x ≤ 15, y ≥ 0, x ≥ 0
Solve the following system of inequalities graphically: x + 2y ≤ 10, x + y ≥ 1, x – y ≤ 0, x ≥ 0, y ≥ 0
Find all pairs of consecutive odd natural number, both of which are larger than 10, such that their sum is less than 40.
How many litres of water will have to be added to 1125 litres of the 45% solution of acid so that the resulting mixture will contain more than 25% but less than 30% acid content?
A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it. The resulting mixture is to be more than 4% but less than 6% boric acid. If there are 640 litres of the 8% solution, how many litres of 2% solution will have to be added?
Write the set of values of x satisfying the inequation (x2 − 2x + 1) (x − 4) < 0.
Write the solution set of the equation |2 − x| = x − 2.
Write the number of integral solutions of \[\frac{x + 2}{x^2 + 1} > \frac{1}{2}\]
Write the solution set of the inequation |x − 1| ≥ |x − 3|.
Solve each of the following system of equations in R.
\[5x - 7 < 3\left( x + 3 \right), 1 - \frac{3x}{2} \geq x - 4\]
Find the graphical solution of the following system of linear inequations:
x – y ≤ 0, 2x – y ≥ − 2
Find the graphical solution of the following system of linear inequations:
3x + 2y ≤ 1800, 2x + 7y ≤ 1400
Solve the following system of inequalities graphically.
2x – y ≥ 1, x – 2y ≤ – 1
Find the linear inequalities for which the shaded region in the given figure is the solution set.
Solve the following system of inequalities `(2x + 1)/(7x - 1) > 5, (x + 7)/(x - 8) > 2`
Find the linear inequalities for which the shaded region in the given figure is the solution set.
Solve the following system of linear inequalities:
3x + 2y ≥ 24, 3x + y ≤ 15, x ≥ 4
Solution set of x ≥ 0 and y ≤ 0 is
