You have 5 liters of Solution A, which is 50% diluted, and 15 liters of Solution B, which is 20% diluted. How much of Solution B must be added to Solution A to make Solution A 55% diluted?(1 point)
Responses
105 liters
105 liters
0.71 liters
0.71 liters
−105
liters
negative 105 liters
The answer is extraneous.
To solve this problem, we can set up an equation based on the information given.
Let x represent the amount of Solution B (in liters) that needs to be added to Solution A.
The total volume of the resulting solution after adding Solution B is 5 + x liters.
The total amount of diluted substance in the resulting solution is 0.55*(5 + x) liters.
The total amount of diluted substance in Solution A is 0.5*5 = 2.5 liters.
The total amount of diluted substance in Solution B is 0.2*15 = 3 liters.
Setting up the equation:
2.5 + 3 = 0.55*(5 + x)
Simplifying the equation:
5.5 = 2.75 + 0.55x
Subtracting 2.75 from both sides:
2.75 = 0.55x
Dividing both sides by 0.55:
5 = x
Therefore, we need to add 5 liters of Solution B to Solution A to make Solution A 55% diluted.
To solve this problem, we can set up an equation based on the desired concentration of the final solution:
(5L * 0.50) + (15L * 0.20) + (x * 0.20) = (5L + x) * 0.55
Simplifying this equation, we get:
2.5L + 3L + 0.2x = 2.75L + 0.55x
Combining like terms, we have:
5.5L + 0.2x = 2.75L + 0.55x
Subtracting 2.75L and 0.2x from both sides of the equation, we get:
5.5L - 2.75L = 0.55x - 0.2x
Simplifying further:
2.75L = 0.35x
To isolate x, we divide both sides of the equation by 0.35:
x = (2.75L) / 0.35
Now, let's substitute the given values:
x = (2.75 * 5) / 0.35
x = 13.75 / 0.35
x ≈ 39.29
Therefore, you will need to add approximately 39.29 liters of Solution B to Solution A to make Solution A 55% diluted.
To solve this problem, we need to use the concept of dilution.
Let's break down the information given:
- Solution A is 50% diluted and we have 5 liters of it.
- Solution B is 20% diluted and we have 15 liters of it.
- We want to find the amount of Solution B that needs to be added to Solution A to make Solution A 55% diluted.
To solve this, we can use the formula for dilution:
(concentration of solution A * volume of solution A) +
(concentration of solution B * volume of solution B) =
(concentration of resulting solution * volume of resulting solution)
We know the following values:
- The concentration of solution A is 50% (0.5).
- The volume of solution A is 5 liters.
- The concentration of solution B is 20% (0.2).
- We want the resulting solution to be 55% diluted (0.55).
Let's plug in these values:
(0.5 * 5) + (0.2 * volume of solution B) = 0.55 * (5 + volume of solution B)
Simplifying the equation:
2.5 + (0.2 * volume of solution B) = 2.75 + 0.55 * volume of solution B
Rearranging the equation:
0.55 * volume of solution B - 0.2 * volume of solution B = 2.75 - 2.5
0.35 * volume of solution B = 0.25
Dividing both sides by 0.35:
volume of solution B = 0.25 / 0.35
volume of solution B ≈ 0.71 liters
Therefore, approximately 0.71 liters of Solution B must be added to Solution A to achieve a 55% dilution. (Option 2)