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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Let's break down the problem step by step.

1. **Initial Orange Drink:**
   - Total volume: 10 liters
   - Fraction of water: 2/3
   - Water in orange drink: \( \frac{2}{3} \times 10 = \frac{20}{3} \) liters

2. **Spilled Orange Drink:**
   - Volume spilled: 1 liter
   - Fraction of water in spilled drink: 2/3
   - Water spilled: \( \frac{2}{3} \times 1 = \frac{2}{3} \) liters

3. **Remaining Orange Drink:**
   - Total volume remaining: \( 10 - 1 = 9 \) liters
   - Water remaining: \( \frac{20}{3} - \frac{2}{3} = \frac{18}{3} = 6 \) liters

4. **Pineapple Drink:**
   - Total volume: 15 liters
   - Fraction of water: 3/5
   - Water in pineapple drink: \( \frac{3}{5} \times 15 = 9 \) liters

5. **Total Remaining Mixture:**
   - Total volume: \( 9 \) (orange) + \( 15 \) (pineapple) = \( 24 \) liters
   - Total water: \( 6 \) (orange) + \( 9 \) (pineapple) = \( 15 \) liters

The amount of water in the remaining 24 liters is \(\boxed{15}\).