A 400 g solution is 25% salt. How much salt must be added to produce a solution that is 40% salt?
To solve this problem, we need to consider the amount of salt in the initial solution and the final desired concentration of salt.
Let's break down the given information:
Initial solution:
- Amount of solution = 400 g
- Salt concentration = 25%
Final desired solution:
- Salt concentration = 40%
To find out how much salt needs to be added, we'll follow these steps:
Step 1: Find the amount of salt in the initial solution:
- Amount of solution = 400 g
- Salt concentration = 25%
- So, the amount of salt in the initial solution is 400 g * 25% = 100 g
Step 2: Calculate the amount of salt needed to reach the final desired concentration:
- Let's assume the amount of salt to be added is x grams.
- When x grams of salt is added, the total amount of salt in the final solution will be 100 g (initial salt) + x g (added salt).
- The total amount of solution will remain 400 g.
- So, the concentration of salt in the final solution will be (100 g + x g) / 400 g = 40%.
Step 3: Solve for x (the amount of salt to be added):
- We can set up an equation based on the concentration of salt in the final solution:
(100 g + x g) / 400 g = 40% = 0.4
- Multiplying both sides of the equation by 400 g gives us:
100 g + x g = 0.4 * 400 g
100 g + x g = 160 g
- Subtracting 100 g from both sides:
x g = 160 g - 100 g
x g = 60 g
So, to produce a solution that is 40% salt, you need to add 60 grams of salt.
400 g solution is 25% salt, i.e. 100 g salt in 300 g water.
A solution of 40% (by weight) is composed of 40% salt, and 60% water.
So for 300g water, we need 5*40=200 g of salt.
We need to add 200-100=100 g of salt to the 400 g solution to make the solution 40%.
Check: water 300g, salt 200g, total 500g
Percentage (by weight) of salt = 200/500=40%.
Note:
This is very well as far as mathematics go. In practice, 100g of water can only dissolve 40g of salt, at 100°C. So 300g of water can only dissolve 120g of salt, with 80g undissolved.