A 19 liter mixture consists by volume of 1 part juice to 18 parts water. If x liters of juice and y liters of water are added to this mixture to make a 54 liter mixture consisting by volume of 1 part juice to 2 parts water, then what is the value of x?
Let's break down the problem step by step:
1. We have a 19-liter mixture consisting of 1 part juice to 18 parts water. This means that in the initial mixture, there is 1/19 of juice and 18/19 of water.
- Juice in the initial mixture = (1/19) * 19 liters = 1 liter
- Water in the initial mixture = (18/19) * 19 liters = 18 liters
2. We are adding x liters of juice and y liters of water to this mixture to make a 54-liter mixture consisting of 1 part juice to 2 parts water.
- Juice in the final mixture = 1/3 of the total volume = (1/3) * 54 liters = 18 liters
- Water in the final mixture = 2/3 of the total volume = (2/3) * 54 liters = 36 liters
3. Since we started with 1 liter of juice and added x liters of juice, the total juice in the final mixture is 1 + x liters.
4. We can set up the equation:
Juice in the final mixture = Juice in the initial mixture + Juice added
18 liters = 1 liter + x liters
18 = 1 + x
Now we can solve the equation to find the value of x:
18 = 1 + x
x = 18 - 1
x = 17
Therefore, the value of x is 17 liters.
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