You need a 45% alcohol solution. On hand, you have a 225 mL of a 85% 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.
Equation:
0.85 * 225 = 0.45 * (225 + x)
Let's break down the information given:
Amount of initial alcohol mixture = 225 mL
Percentage of alcohol in the initial mixture = 85%
Amount of pure water to be added = x mL
To find the equation, we can use the concept of the amount of alcohol being constant before and after the mixture.
The amount of alcohol in the initial mixture can be calculated as follows:
Amount of alcohol = 225 mL * (85/100) = 191.25 mL
The amount of alcohol in the final mixture (after adding water) will remain the same, which is 191.25 mL.
To find the amount of pure water needed, we need to consider that the volume of the final mixture will be the sum of the initial mixture and the added water:
Total volume of the final mixture = 225 mL + x mL
Now, we can set up the equation:
Alcohol in the initial mixture = Alcohol in the final mixture
191.25 mL = 45% * (225 mL + x mL)
Let's simplify the equation:
191.25 = 0.45 * (225 + x)
Now, we can solve for x by isolating it on one side of the equation:
191.25 = 101.25 + 0.45x
Subtracting 101.25 from both sides:
90 = 0.45x
Dividing both sides by 0.45:
x = 200 mL
Therefore, you will need to add 200 mL of pure water to obtain the desired 45% alcohol solution.