You need a 30% alcohol solution. On hand, you have a 270 mL of a 70% alcohol mixture. How much pure water will you need to add to obtain the desired solution?
A) Write an equation using the information as it is given above that can be used to solve this problem. Use x as your variable to represent the amount of pure water you need to use.
How much mL of pure water
How much mL of the desired 30% solution
Let x represent the amount of pure water needed to obtain the desired solution.
The total volume of the solution after adding the water will be 270 mL + x mL.
Since we want a 30% alcohol solution, the amount of alcohol in the solution can be represented as 30% of the total volume of the solution.
Thus, the equation can be written as:
0.3(270 + x) = 0.7(270)
This equation represents the amount of alcohol in the final solution (30% of the total volume) equal to the amount of alcohol in the initial mixture (70% of the initial volume).
To solve this equation, we can multiply both sides by 10 to get rid of the decimals:
3(270 + x) = 7(270)
Now, we can distribute and simplify:
810 + 3x = 1890
Next, we subtract 810 from both sides:
3x = 1080
Finally, we divide both sides by 3 to solve for x:
x = 360
Therefore, you will need to add 360 mL of pure water to obtain the desired 30% solution.
The amount of the desired 30% solution will be 270 mL + 360 mL = 630 mL.