Grade 9Algebra

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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 …..

Please explain its answer as fast as possible

jeeva

9 Years agoGrade 9

2 Answers

Saurabh Koranglekar

6 Years ago

To determine how many litres of water need to be added to a 1125-litre solution containing 45% acid in order to achieve a final concentration between 25% and 30% acid, we can break this down into a few logical steps.

Understanding the Initial Condition

The initial volume of the solution is 1125 litres, and it contains 45% acid. To find out how much acid is present in this solution, we can calculate:

Amount of acid = 45% of 1125 litres
Amount of acid = 0.45 * 1125 = 506.25 litres of acid

Setting Up the Equation for Water Addition

Let’s denote the amount of water we need to add as x litres. After adding water, the total volume of the solution becomes:

Total volume = 1125 litres + x litres

The concentration of acid in the new solution is given by the ratio of the amount of acid to the total volume:

Concentration of acid = (Amount of acid) / (Total volume)
Concentration of acid = 506.25 / (1125 + x)

Establishing the Concentration Range

We want the concentration of acid to be more than 25% but less than 30%. This gives us two inequalities to work with:

(1) 506.25 / (1125 + x) > 0.25
(2) 506.25 / (1125 + x) < 0.30

Solving the First Inequality

From the first inequality:

506.25 > 0.25 * (1125 + x)
506.25 > 281.25 + 0.25x
506.25 - 281.25 > 0.25x
225 > 0.25x
x < 900

Solving the Second Inequality

Now for the second inequality:

506.25 < 0.30 * (1125 + x)
506.25 < 337.5 + 0.30x
506.25 - 337.5 < 0.30x
168.75 < 0.30x
x > 562.5

Finding the Range for x

Now we can combine our results:

562.5 < x < 900

This means that to achieve a concentration of acid between 25% and 30%, you need to add more than 562.5 litres of water but less than 900 litres.

Practical Implication

In practical terms, if you want to ensure the acid concentration stays within this range, you can add any amount of water between these two limits. For instance, if you decide to add 600 litres, you will end up with a solution that meets the criteria.

So, the final answer is: you need to add more than 562.5 litres and less than 900 litres of water to the 1125-litre solution to get the desired acid concentration.

Arun

6 Years ago

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)

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)
506.25
506.25
168.75
562.5

The final answer, then, is 562.5

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.

Hope it helps