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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We are given:

- **10 liters of orange drink**, which is **two-thirds water**.
- **15 liters of pineapple drink**, which is **three-fifths water**.
- **1 liter of the orange drink is spilled** before mixing.
- Then, the remaining orange drink is added to the pineapple drink, resulting in **24 liters total** (since 10 − 1 = 9 liters orange left, and 9 + 15 = 24 liters total — checks out).

We are to find: **How much water is in the remaining 24 liters?**

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### Step 1: Water in original orange drink

Original orange drink: 10 liters, 2/3 water.

Water in orange = $ \frac{2}{3} \times 10 = \frac{20}{3} $ liters.

But 1 liter is spilled. Since it's a uniform mixture, the spilled 1 liter has the same concentration: 2/3 water.

So water spilled = $ \frac{2}{3} \times 1 = \frac{2}{3} $ liters.

Therefore, **water remaining in orange drink** = $ \frac{20}{3} - \frac{2}{3} = \frac{18}{3} = 6 $ liters.

Alternatively: Remaining orange drink = 9 liters, 2/3 water → $ \frac{2}{3} \times 9 = 6 $ liters. ✅

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### Step 2: Water in pineapple drink

Pineapple drink: 15 liters, 3/5 water.

Water = $ \frac{3}{5} \times 15 = 9 $ liters.

No spillage here.

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### Step 3: Total water in final mixture

Total water = water from remaining orange + water from pineapple  
= $ 6 + 9 = 15 $ liters.

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### Final Answer:

\boxed{15}