You need 490 mL of a 40% alcohol solution. On hand, you have a 70% alcohol mixture. How much of the 70% alcohol mixture and pure water will you need to obtain the desired solution?
Well, let me calculate that for you. To make a 40% alcohol solution, you'll need to mix the 70% alcohol mixture with water. Let's assume you need x mL of the 70% alcohol mixture.
Now, the amount of alcohol in the 70% solution is 0.70x mL. And since you need 490 mL of a 40% solution, the amount of alcohol needed is 0.40 * 490 mL = 196 mL.
So, we can set up the equation 0.70x + 0(490 - x) = 196, where 490 - x represents the amount of water we need to add.
Simplifying the equation, we get 0.70x = 196. Divide both sides by 0.70, and you get x ≈ 280.
So, you'll need approximately 280 mL of the 70% alcohol mixture and the remaining amount (490 - 280) mL of pure water.
Remember, though, these calculations are assuming you won't drink all this alcohol by yourself!
To determine the quantities of the 70% alcohol mixture and pure water needed to obtain the desired solution, follow these steps:
Step 1: Let's assume you need x mL of the 70% alcohol mixture.
Step 2: Since the total volume required is 490 mL and you already have x mL of the 70% alcohol mixture, the amount of pure water needed will be 490 - x mL.
Step 3: Multiply the volume of the 70% alcohol mixture (x mL) by its concentration (70%) to determine the amount of alcohol in the mixture: 0.70 * x.
Step 4: Multiply the volume of pure water (490 - x mL) by its concentration (0%) to determine the amount of alcohol in the water: 0 * (490 - x).
Step 5: The total amount of alcohol in the final mixture should be (0.40 * 490) mL since you need a 40% alcohol solution.
Step 6: Set up an equation using the information from steps 3, 4, and 5: 0.70x + 0(490 - x) = 0.40 * 490.
Step 7: Solve the equation: 0.70x = 0.40 * 490.
Step 8: Divide both sides of the equation by 0.70: x = (0.40 * 490) / 0.70.
Step 9: Calculate x.
Using these steps, you will find the quantities of the 70% alcohol mixture and pure water needed to obtain the desired solution.
To solve this problem, we need to use the concept of mixing solutions. Let's break it down step-by-step:
Step 1: Define the variables:
Let's denote:
- x as the amount (in mL) of the 70% alcohol mixture needed
- y as the amount (in mL) of pure water needed
Step 2: Write the equation based on the alcohol content:
Since we need a 40% alcohol solution, we can set up the following equation by considering the alcohol content in the 70% alcohol mixture:
0.70x + 0 * y = 0.40 * 490
The equation represents the sum of the amount of alcohol in the 70% alcohol mixture and the amount of alcohol in the pure water (which is 0 because water has no alcohol). This equation says that the total amount of alcohol in the desired solution (left side) must equal the amount of alcohol required for a 40% solution (right side).
Step 3: Solve the equation:
0.70x + 0 = 0.40 * 490
0.70x = 0.40 * 490
0.70x = 196
Divide both sides of the equation by 0.70:
x = 196 / 0.70
x ≈ 280
So, you will need approximately 280 mL of the 70% alcohol mixture.
Step 4: Find the amount of pure water:
We can find the amount of pure water needed by subtracting the amount of the 70% alcohol mixture from the total desired volume:
y = 490 - 280
y = 210
Therefore, you will need 280 mL of the 70% alcohol mixture and 210 mL of pure water to obtain a 490 mL solution of 40% alcohol.
0.40 * 490 = 196 mL of pure alcohol needed
196 mL = 0.70 * x mL of 0.7
x = 280 mL of 70%
490 - 280 = 210 mL of H2O