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.

×