Question

how many litres of water will have to be added to 1125
liters of the 45 % solution of acid so that the resulting
mixture will contain more than 25% but less than 30% acid
content

Answer 1

The original solution is 1125 litres of 45% solution. This means 45% of the 1125 litres is acid, the rest is water. The first thing you need to do is find the litres of acid. (0.45)(1125) = 506.25. There are 506.25 litres of acid in the solution. Since we will be adding only water, the litres of acid will not change. The problem can be solved with two inequalities (one for the weaker solution and one for the stronger solution) or with a single, compound inequality. 

For the weaker solution, we need to find a total number of litres so 506.25 is 25% of the total. There are many ways to do this, one is: 

Let x liters (l) of water is required to be added. 

Then, total mixture = (x + 1125) liters
 
It is evident that the amount of acid contained in the resulting mixture is 45% of 1125 liters(l) . 

This resulting mixture will contain more than 25% but less than 30% acid content. 
∴30% of (1125 + x) > 45% of 1125 

And, 25% of (1125 + x) < 45% of 1125 

30% of (1125 + x) > 45% of 1125 

Calculations 

506.25/(1125 + x) >= .25 Solving for x we get 
506.25 >= (.25)(1125 + x) 
506.25 >= 281.25 + .25x 
225 >= .25x 
900 >= x. So we need to add 900 litres to make the weaker solution; this is the most we can add and still be within the range stated for the problem. 

For the stronger solution, 

506.25/(1125 + x) <= .3 
506.25 <= (1125 + x)(.3) 
506.25 <= 337.5 + .3x 
168.75 <= .3x 
562.5 <= x. So we need to add at least 562.5 litres, this will make the stronger solution. 

The final answer, then, is 562.5 <= x <= 900

Thus, the required number of liters (L) of water that is to be added will have to be more than 562.5 but less than 900.