Final answer:
To solve the problem, use the equation (concentration of solution A)(volume of solution A) + (concentration of solution B)(volume of solution B) = (concentration of final solution)(total volume of final solution). Plug in the given values, then simplify and solve the equation to find the relationship between the volume of solution B and the total volume of the final solution.
Step-by-step explanation:
To solve this problem, we can use the equation:
(concentration of solution A)(volume of solution A) + (concentration of solution B)(volume of solution B) = (concentration of final solution)(total volume of final solution)
Let's use the given information:
- Concentration of solution A (0.5%)
- Concentration of solution B (2%)
- Concentration of final solution (0.65%)
- Volume of solution B (unknown, represented as x)
- Total volume of final solution (unknown, represented as y)
Plugging in the values into the equation, we have:
(0.005)(x) + (0.02)(y - x) = (0.0065)(y)
Simplifying and solving the equation gives us:
0.005x + 0.02y - 0.02x = 0.0065y
0.0165y - 0.015x = 0.005x
0.0115y = 0.02x
0.023y = 2x
23y = 200x
To solve for y, we can choose a value for x (the volume of solution B) and find the corresponding value for y (the total volume of the final solution).