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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Alright, let's tackle this problem step by step. I'll break it down to understand how much water is in the remaining 24 liters after mixing the orange and pineapple drinks with a spill.

### Understanding the Problem

We have two drinks:
1. **Orange Drink**: 
   - Total volume: 10 liters
   - Water content: Two-thirds of the total volume
2. **Pineapple Drink**: 
   - Total volume: 15 liters
   - Water content: Three-fifths of the total volume

We're going to mix these two drinks, but during the pouring, we spill 1 liter of the orange drink. After mixing and spilling, the total volume is 24 liters. We need to find out how much water is in this final 24 liters.

### Step 1: Calculate the Amount of Water in the Orange Drink

The orange drink is 10 liters total, and two-thirds of it is water.

\[ \text{Water in orange drink} = \frac{2}{3} \times 10 \text{ liters} \]
\[ \text{Water in orange drink} = \frac{20}{3} \text{ liters} \]
\[ \text{Water in orange drink} \approx 6.\overline{6} \text{ liters} \]

### Step 2: Calculate the Amount of Non-Water in the Orange Drink

The remaining one-third of the orange drink is not water.

\[ \text{Non-water in orange drink} = \frac{1}{3} \times 10 \text{ liters} \]
\[ \text{Non-water in orange drink} = \frac{10}{3} \text{ liters} \]
\[ \text{Non-water in orange drink} \approx 3.\overline{3} \text{ liters} \]

### Step 3: Calculate the Amount of Water in the Pineapple Drink

The pineapple drink is 15 liters total, and three-fifths of it is water.

\[ \text{Water in pineapple drink} = \frac{3}{5} \times 15 \text{ liters} \]
\[ \text{Water in pineapple drink} = \frac{45}{5} \text{ liters} \]
\[ \text{Water in pineapple drink} = 9 \text{ liters} \]

### Step 4: Calculate the Amount of Non-Water in the Pineapple Drink

The remaining two-fifths of the pineapple drink is not water.

\[ \text{Non-water in pineapple drink} = \frac{2}{5} \times 15 \text{ liters} \]
\[ \text{Non-water in pineapple drink} = \frac{30}{5} \text{ liters} \]
\[ \text{Non-water in pineapple drink} = 6 \text{ liters} \]

### Step 5: Account for the Spilled Orange Drink

We spill 1 liter of the orange drink. We need to determine how much of that spilled liter is water and how much is non-water.

The orange drink's water and non-water are in a ratio of 2:1 (since it's two-thirds water and one-third non-water).

\[ \text{Water in spilled orange drink} = \frac{2}{3} \times 1 \text{ liter} = \frac{2}{3} \text{ liters} \]
\[ \text{Non-water in spilled orange drink} = \frac{1}{3} \times 1 \text{ liter} = \frac{1}{3} \text{ liters} \]

### Step 6: Calculate the Remaining Orange Drink After Spilling

Original orange drink: 10 liters
Spilled: 1 liter
Remaining orange drink: 10 - 1 = 9 liters

But we've already accounted for the water and non-water in the spilled part, so the remaining orange drink's water and non-water are:

\[ \text{Remaining water in orange drink} = \frac{20}{3} - \frac{2}{3} = \frac{18}{3} = 6 \text{ liters} \]
\[ \text{Remaining non-water in orange drink} = \frac{10}{3} - \frac{1}{3} = \frac{9}{3} = 3 \text{ liters} \]

So, the remaining orange drink is 6 liters water and 3 liters non-water, totaling 9 liters.

### Step 7: Combine the Remaining Orange Drink and the Pineapple Drink

Now, we mix:
- Remaining orange drink: 6 liters water + 3 liters non-water
- Pineapple drink: 9 liters water + 6 liters non-water

Total water in the mixture:
\[ 6 \text{ liters (orange)} + 9 \text{ liters (pineapple)} = 15 \text{ liters} \]

Total non-water in the mixture:
\[ 3 \text{ liters (orange)} + 6 \text{ liters (pineapple)} = 9 \text{ liters} \]

Total volume of the mixture:
\[ 15 \text{ liters (water)} + 9 \text{ liters (non-water)} = 24 \text{ liters} \]

This matches the given total volume after mixing and spilling.

### Step 8: Determine the Amount of Water in the Final 24 Liters

From the above calculation, the total water in the final mixture is 15 liters.

### Verification

Let me double-check the calculations to ensure no