Making Lemonade?

Algebra Level 5

Alice and Bob are given a \(2000\) mL pitcher of water and an empty bottle. First, Alice pours \(L\) mL of lemon juice into the pitcher, where \(L\) is a positive rational number. She mixes well, then pours \(L\) mL of the resulting mixture into the bottle. Afterwards, Bob pours \(1000\) mL of pure water into the pitcher, mixes well, and pours \(1000\) mL of the resulting mixture into the bottle. Finally, the contents of the bottle are thoroughly mixed. If the mixture in the bottle is \(20\%\) lemon juice, find the integer closest to \(L\).

Notes:

When Alice and Bob mix well, the concentration of lemon juice/water is the same throughout the mixture.

Lemon juice is \(100\%\) lemon juice and water is \(0\%\) lemon juice.

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