A solution whose volume is 80% liters is made up of 40% of water and 60% of alcohol,When x liters of water is added the percentage of alcohol drops to 40% Find X
Where is the answer
Let's solve this step-by-step:
1. Let's assume the initial volume of the solution is V liters.
2. Given that the solution is 80% liters, 80% of V liters is alcohol + water.
So, 0.8V = alcohol + water.
3. It is also given that the solution is made up of 40% water and 60% alcohol.
So, 40% of 0.8V liters is water, and 60% of 0.8V liters is alcohol.
We can write these equations as:
water = 0.4 * 0.8V
alcohol = 0.6 * 0.8V
4. It is also stated that when x liters of water is added, the percentage of alcohol drops to 40%.
So, the new volume of water after adding x liters would be (0.4 * 0.8V) + x liters.
And the new volume of alcohol would be (0.6 * 0.8V) liters.
5. We can now set up an equation to solve for x:
(0.6 * 0.8V) / (0.4 * 0.8V + x) = 0.4
Simplifying this equation, we have:
(0.6 / (0.4 * 0.8V + x)) = 0.4
0.6 = 0.4 * (0.4 * 0.8V + x)
0.6 = 0.16V + 0.4x
0.4x = 0.6 - 0.16V
x = (0.6 - 0.16V) / 0.4
So, the value of x is (0.6 - 0.16V) / 0.4.
To solve this problem, we can set up a mathematical equation based on the given information.
Let's assume that the total volume of the solution before adding water is T liters.
According to the problem, the solution is initially 40% water and 60% alcohol. Thus, the amount of water in the solution before adding any extra water is 40% of T liters, which can be represented as 0.4T. Similarly, the amount of alcohol in the solution is 60% of T liters, which can be represented as 0.6T.
Now, when x liters of water is added to the solution, the volume of water in the solution becomes (0.4T + x) and the volume of alcohol remains the same at 0.6T liters.
The new solution is now stated to be 40% alcohol. This means that the volume of alcohol should be 40% of the total solution volume. We can write this as:
0.4*(0.4T + x) = 0.6T
Now, let's solve this equation to find the value of x.
First, simplify the equation:
0.16T + 0.4x = 0.6T
Rearrange the equation:
0.4x = 0.6T - 0.16T
0.4x = 0.44T
Divide both sides by 0.4:
x = 0.44T / 0.4
Simplify further:
x = 1.1T
Therefore, the amount of water (x liters) that needs to be added to the solution is 1.1 times the initial total solution volume (T).
You have mangled the question, but if I parse the meaning correctly, you need to check the amount of alcohol before and after mixing in the water:
.60(80) = .40(80+x)