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)
1. 105 liters
2. The answer is extraneous
3. -105 liters
4. 0.71 liters
Let's set up the equation to solve for the amount of Solution B needed.
Let x represent the amount of Solution B needed in liters.
The total amount of the solution after mixing is (5 + x) liters.
The equation is:
0.5(5) + 0.2(15) = 0.55(5 + x)
2.5 + 3 = 2.75 + 0.55x
5.5 = 2.75 + 0.55x
2.75 = 0.55x
Dividing both sides by 0.55 gives:
x = 5
Therefore, the correct answer is 5 liters. So, 5 liters of Solution B must be added to Solution A to make Solution A 55% diluted.
To solve this problem, we can create an equation to represent the dilution of Solution A. Let x represent the amount of Solution B we need to add.
The equation for the dilution is:
(5 liters)(50%) + (x liters)(20%) = (5 + x liters)(55%)
Now we can solve for x:
(0.5)(5) + (0.2)(x) = (0.55)(5 + x)
2.5 + 0.2x = 2.75 + 0.55x
0.2x - 0.55x = 2.75 - 2.5
-0.35x = 0.25
x = 0.25 / -0.35
x ≈ -0.71 liters
Since it doesn't make sense to have a negative amount of Solution B added, the answer must be extraneous.
Therefore, the correct answer is 2. The answer is extraneous.
To determine how much of Solution B must be added to Solution A, we can use the concept of concentrations and dilutions. Let's go step by step:
First, let's calculate the volume of the final solution, when the concentration of Solution A is 55%. We know that Solution A has an initial volume of 5 liters and is 50% diluted. This means that 50% of the solution is solute (active ingredient) and the remaining 50% is solvent (usually water). Therefore, the active ingredient in Solution A is 5 liters * 50% = 2.5 liters.
To achieve a final concentration of 55%, the active ingredient in the final solution should be 55% of the total volume. We'll call the volume of Solution B that needs to be added "x" liters, so the total volume of the final solution is (5 + x) liters. The total volume of the active ingredient in the final solution is (5 + x) liters * 55% = 0.55(5 + x) liters.
Next, let's determine the amount of active ingredient in Solution B. We know that Solution B has an initial volume of 15 liters and is 20% diluted. This means that 20% of the solution is the active ingredient, so the active ingredient in Solution B is 15 liters * 20% = 3 liters.
Now, we can set up an equation to find the amount of Solution B needed to achieve the desired concentration. The total amount of active ingredient in the final solution should be equal to the sum of the active ingredients in Solution A and Solution B.
0.55(5 + x) liters = 2.5 liters + 3 liters
0.55(5 + x) = 5.5
2.75 + 0.55x = 5.5
0.55x = 5.5 - 2.75
0.55x = 2.75
x = 2.75 / 0.55
x = 5
Therefore, the amount of Solution B that needs to be added to Solution A to make Solution A 55% diluted is 5 liters. This means that the correct answer is option 1.