gsm8k-0020

# GSM8K Problem 21

I have 10 liters of orange drink that are two-thirds water and I wish to add it to 15 liters of pineapple drink that is three-fifths water. But as I pour it, I spill one liter of the orange drink. How much water is in the remaining 24 liters?

Reason step by step, then give ONLY the final answer on the last line as \boxed{ANSWER}.

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Here is the step-by-step reasoning:

1.  **Analyze the Orange Drink:**
    *   Total volume: 10 liters.
    *   Water content: $\frac{2}{3}$ of the volume.
    *   Amount of water: $10 \times \frac{2}{3} = \frac{20}{3}$ liters.

2.  **Analyze the Pineapple Drink:**
    *   Total volume: 15 liters.
    *   Water content: $\frac{3}{5}$ of the volume.
    *   Amount of water: $15 \times \frac{3}{5} = 9$ liters.

3.  **Account for the Spill:**
    *   You spill 1 liter of the orange drink while pouring.
    *   Since the drink is a mixture, the spilled liter contains the same proportion of water as the rest of the drink ($\frac{2}{3}$ water).
    *   Remaining volume of orange drink: $10 - 1 = 9$ liters.
    *   Remaining water in the orange drink: $9 \times \frac{2}{3} = 6$ liters.
    *   (Alternatively, subtract the water lost: $\frac{20}{3} - \frac{2}{3} = \frac{18}{3} = 6$ liters).

4.  **Calculate Total Water in the Mixture:**
    *   The final mixture consists of the remaining 9 liters of orange drink and the full 15 liters of pineapple drink.
    *   Total volume: $9 + 15 = 24$ liters (which matches the problem statement).
    *   Total water = (Water in remaining orange drink) + (Water in pineapple drink).
    *   Total water = $6 + 9 = 15$ liters.

\boxed{15}