Answer:
<em>x=4.8473 cups</em>
Step-by-step explanation:
<u>Concentration of Liquids </u>
It measures the amount of substance present in a mixture, often expressed as %. If there is an volume x of a substance in a total volume mix of y, the concentration is given by
It we take a sample of that mixture, we must consider that we are getting only the substance, but all the mixture (assumed it has been uniformly mixed). For example, if we take a glass of liquid from a 80% mixture of juice, the glass will also have a 80% of juice.
Let's solve the problem sequentially. At first, let's assume all the container is full of x cups of juice. Its concentration is 100%. Now let's take 1 cup of pure juice and replace it by 1 cup of pure water. The new amount of juice in the container is
x-1 cups of juice.
The new concentration is
The boy takes a second cup of liquid, but this time it's not pure juice, it has a mixture of juice and water with a concentration computed above. Now the amount of juice is
cups of juice.
Simplifying, the cups of juice are
The new concentration is
For the third time, we now have
cups of juice.
Simplifying, the final amount of juice is
And the final concentration is
According to the conditions of the question, this must be equal to 50% (0.5)
Taking cubic roots
Operating and joining like terms
Solving for x
Let's test our result
Final concentration: