A 400 g solution is 25% salt. How much salt must be added to produce a solution that is 40% salt?
To find out how much salt must be added, we need to determine the amount of salt in the initial solution and then calculate the additional amount needed to reach the desired concentration.
Let's break down the problem step by step:
Step 1: Determine the amount of salt in the initial solution.
The initial solution weighs 400 g and has a concentration of 25% salt.
So, the amount of salt in the initial solution can be calculated as:
Amount of salt in initial solution = 25% of 400 g
To calculate a percentage, we convert it to its decimal form by dividing it by 100:
25% = 25/100 = 0.25
Now, we can find the amount of salt in the initial solution by multiplying 400 g by 0.25:
Amount of salt in initial solution = 400 g * 0.25
Step 1 result: The initial solution contains 100 g of salt.
Step 2: Determine the additional amount of salt needed to reach the desired concentration.
We want to produce a solution that is 40% salt. Since we already have 100 g of salt in the initial solution, we need to find out how much more salt we need to add.
Let's denote the additional amount of salt needed as "x" (in grams).
The total weight of the final solution (after adding the salt) will be the sum of the initial solution weight (400 g) and the additional salt (x).
So, the equation can be set up as follows:
Total salt in final solution = Salt in initial solution + Additional salt
Since the final concentration we want is 40%, we can express it as a decimal (40/100 = 0.40).
So, the equation becomes:
0.40 * (400 g + x) = 100 g + x
Step 2 result: We have set up the equation to find the additional amount of salt needed.
Now, we can solve the equation to find the value of "x" (the additional amount of salt needed).
Let's solve it:
0.40 * (400 g + x) = 100 g + x
expanding the equation gives us:
160 g + 0.40x = 100 g + x
Rearranging the equation to isolate "x" gives us:
0.40x - x = 100 g - 160 g
-0.60x = -60 g
Dividing both sides of the equation by -0.60 gives us:
x = (-60 g) / (-0.60)
x = 100 g
Step 3 result: The additional amount of salt needed is 100 grams.
Therefore, to produce a solution that is 40% salt, you must add an additional 100 grams of salt.