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?
More than 562.5 litres but less than 900 litres of water should be added.
Explanation
This question follows the same pattern as Example 13 in the textbook. The key concept is that when water is added to an acid solution, the amount of acid remains constant while the total volume increases. We set up two inequalities representing the lower bound (25%) and upper bound (30%) of acid concentration in the final mixture, then solve for the unknown quantity of water.
Solution Steps
Step 1: Let x litres of water be added to the solution.
Step 2: Calculate the amount of acid in the original solution: 45% of 1125 litres = (45/100) × 1125 = 506.25 litres
Step 3: Total volume of resulting mixture = (1125 + x) litres
Step 4: The acid content in the resulting mixture must be more than 25% but less than 30%. Therefore: 25% < (Acid amount / Total volume) × 100 < 30%
Step 5: Set up the inequalities: 25 < (506.25 / (1125 + x)) × 100 < 30
Step 6: Solve the first inequality (more than 25%): 25 < (506.25 / (1125 + x)) × 100 25/100 < 506.25 / (1125 + x) 0.25 × (1125 + x) < 506.25 281.25 + 0.25x < 506.25 0.25x < 225 x < 900
Step 7: Solve the second inequality (less than 30%): (506.25 / (1125 + x)) × 100 < 30 506.25 / (1125 + x) < 0.30 506.25 < 0.30 × (1125 + x) 506.25 < 337.5 + 0.30x 168.75 < 0.30x 562.5 < x
Step 8: Combining both results: 562.5 < x < 900 Thus, the water to be added should be more than 562.5 litres but less than 900 litres.