Step-by-step explanation:
To prepare 500 mL of D12.5W, you would need to mix D5W and D70W in the correct proportions. The concentration of the final solution is the sum of the concentrations of the two solutions.
Let's assign variables to the unknown quantities:
Let x be the volume of D5W needed (in mL).
Let y be the volume of D70W needed (in mL).
Given that the final concentration is D12.5W, we can set up the following equation:
5x + 70y = 12.5 * 500
This equation represents the conservation of solute (in this case, dextrose) in the solution.
Now, we solve this equation to find the values of x and y:
5x + 70y = 6250
Divide the equation by 5 to simplify:
x + 14y = 1250
To find the values that satisfy this equation, we can check the provided options:
a) 400 mL of D5W and 100 mL of D70W:
5(400) + 70(100) = 2000 + 7000 = 9000 (not equal to 6250)
b) 58 mL of D5W and 422 mL of D70W:
5(58) + 70(422) = 290 + 29540 = 29830 (not equal to 6250)
c) 100 mL of D5W and 400 mL of D70W:
5(100) + 70(400) = 500 + 28000 = 28500 (not equal to 6250)
d) 422 mL of D5W and 58 mL of D70W:
5(422) + 70(58) = 2110 + 4060 = 6170 (not equal to 6250)
None of the options satisfy the equation.
Based on the given options, it seems that there is an error, and none of the options provided are the correct solution.