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}.

<!-- imported from openai/gsm8k (test) -->

I need to find the amount of water in the final mixture after spilling some orange drink.

Let me break this down step by step:

Step 1: Calculate the amount of water in the original orange drink.
- Orange drink: 10 liters total
- Two-thirds is water
- Water in orange drink = (2/3) × 10 = 20/3 liters

Step 2: Calculate the amount of water in the original pineapple drink.
- Pineapple drink: 15 liters total
- Three-fifths is water
- Water in pineapple drink = (3/5) × 15 = 9 liters

Step 3: Account for the spill.
- I spill 1 liter of orange drink
- This means I'm left with 10 - 1 = 9 liters of orange drink
- The spilled liter contains the same proportion of water
- Water in spilled liter = (2/3) × 1 = 2/3 liters
- Water remaining in orange drink = 20/3 - 2/3 = 18/3 = 6 liters

Step 4: Calculate the total volume and water in the final mixture.
- Final volume = (9 liters of orange drink) + (15 liters of pineapple drink) = 24 liters
- Total water = (6 liters from remaining orange drink) + (9 liters from pineapple drink) = 15 liters

Therefore, there are 15 liters of water in the remaining 24 liters.

\boxed{15}