how many liters of water will have to be added to 1125 liters of 45% solution of acid so that the resulting mixture will contain more than 25% but less than 30% acid content.
(1125+x)*25 < 1125*45 < (1125+x)*30
562.5 < x < 900
Let x litres of water will add to 1125 litres of 45% sol. So it give results mixture will contain more than 25% but less than 30% acid content.
(1125 + x)25< 1125*45 <(1125 + x)30 28125+25x<50625< 33750+30x 25x<22500 or 30x>16875 x<900 or x>562.5
Answer:
Let x litres of water will add to 1125 litres of 45% sol. So it give results mixture will contain more than 25% but less than 30% acid content.
(1125 + x)25< 1125*45 <(1125 + x)30 28125+25x<50625< 33750+30x 25x<22500 or 30x>16875 x<900 or x>562.5
Let x litres of water is required to be added.
Then, total mixture = ( x + 1125) litres
It is evident that the amount of acid contained in the resulting mixture is 45% of 1125 litres.
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
25% of (1125 + x ) < 45% of 1125
∴562.5 < x < 900
Thus, the required number of litres of water that is to be added will have to be more than 562.5 but less than 900.
To solve this problem, we need to find out how many liters of water should be added to a 1125 liters 45% acid solution to get a resulting mixture with an acid content between 25% and 30%.
Let's break down the problem step by step:
1. Find the acid content in the resulting mixture:
The initial solution contains 1125 liters of a 45% acid solution. This means there are 1125 liters * (45/100) = 506.25 liters of acid in the solution.
2. Determine the acid content range for the resulting mixture:
The goal is to have an acid content between 25% and 30%. This means the acid content should be greater than (25/100) and less than (30/100).
3. Set up an equation to solve for the amount of water needed:
Let's assume that x liters of water need to be added to the initial solution.
So, the total volume of the resulting mixture will be 1125 liters + x liters.
The amount of acid in the resulting mixture will remain the same as the initial solution, which is 506.25 liters.
The total volume of the resulting mixture will be the initial volume plus the added volume of water, which is (1125 + x) liters.
The acid content in the resulting mixture will be the amount of acid divided by the total volume of the mixture:
Acid content = (506.25 liters) / (1125 liters + x liters)
4. Solve the inequality:
We need to determine the range of values for x that will give us a resulting mixture with an acid content between 25% and 30%.
So, we can set up the following inequality:
0.25 < (506.25 liters) / (1125 liters + x liters) < 0.30
5. Solve the inequality to find the range for x:
To solve the inequality, we can multiply all the terms by (1125 + x) to get rid of the denominator:
0.25 * (1125 + x) < 506.25 liters < 0.30 * (1125 + x)
Now we can solve for x.