A 75% alcohol concentration mixture of water and alcohol was made by mixing 30ml of pure alcohol with 150 ml of original mixture of water and alcohol. what was the alcohol concentration of the orignal mixture
The amount of water has not changed.
Since the final solution is 180 ml and is 75% alcohol, 25% or 45 ml must be water.
So that 45 ml of water must have been in the original 150 ml of the mixture which means 105 ml must have been alcohol
then the alcohol concentration of the original mixture was 105/150 or 70%
To solve this problem, we need to understand the concept of mixtures and their components. In this case, we have a mixture of water and alcohol. Let's break down the steps to find the alcohol concentration of the original mixture:
1. Start by identifying the final solution. The total volume of the final solution is 180 ml.
2. We know that the final solution is 75% alcohol. This means that 75% of the total volume is alcohol, and the remaining 25% is water.
3. Calculate the amount of water in the final solution. Since 25% of 180 ml is water, we can calculate it by multiplying 180 ml by 25%, which is equal to 45 ml.
4. Now, we need to determine how much alcohol is in the final solution. Since the total volume is 180 ml and the amount of water is 45 ml, we can subtract the volume of water from the total volume: 180 ml - 45 ml = 135 ml.
5. So, the final solution contains 135 ml of alcohol.
6. We are given that 30 ml of pure alcohol was added to the original mixture. Thus, this 30 ml must be part of the 135 ml of alcohol in the final solution.
7. To find the amount of alcohol in the original mixture, we subtract the 30 ml from the total alcohol in the final solution: 135 ml - 30 ml = 105 ml.
8. Finally, we divide the amount of alcohol in the original mixture by the total volume of the original mixture. In this case, the original mixture volume is 150 ml.
9. Therefore, the alcohol concentration of the original mixture is 105 ml / 150 ml, which simplifies to 7/10 or 70%.
So, the alcohol concentration of the original mixture was 70%.