A bottle completely filled with water weighed 2.1kg. After 2/3 of the water was used up, the bottle with the remaining water weighed 800g. What was the mass of the bottle in grams?

Let's solve the problem step by step.

### Step 1: Define the Variables
- Let \( m_b \) be the mass of the empty bottle.
- Let \( m_w \) be the mass of the water when the bottle is full.

### Step 2: Set Up the Equations
1. **When the bottle is full:**
   \[
   m_b + m_w = 2100 \, \text{g} \quad \text{(since 2.1 kg = 2100 g)}
   \]
   
2. **When 2/3 of the water is used up:**
   \[
   m_b + \frac{1}{3}m_w = 800 \, \text{g}
   \]

### Step 3: Solve the Equations
Subtract the second equation from the first to eliminate \( m_b \):

\[
(m_b + m_w) - (m_b + \frac{1}{3}m_w) = 2100 \, \text{g} - 800 \, \text{g}
\]

This simplifies to:

\[
m_w - \frac{1}{3}m_w = 1300 \, \text{g}
\]

\[
\frac{2}{3}m_w = 1300 \, \text{g}
\]

Now, solve for \( m_w \):

\[
m_w = 1300 \times \frac{3}{2} = 1950 \, \text{g}
\]

### Step 4: Find the Mass of the Bottle
Using the value of \( m_w \) in the first equation:

\[
m_b + 1950 = 2100 \, \text{g}
\]

\[
m_b = 2100 - 1950 = 150 \, \text{g}
\]

### Final Answer:
The mass of the bottle is **150 grams**.

Would you like more details, or do you have any questions? Here are some related questions you might find interesting:

1. What would the mass of the bottle be if only half of the water remained?
2. How would the problem change if the water used had a different density?
3. If the bottle's mass was given instead, how would you find the mass of the water?
4. How would evaporation affect this scenario if it were not negligible?
5. Can this type of problem be generalized to any liquid in a container?

**Tip:** Always make sure to convert units to the same system (grams, kilograms, etc.) before solving equations involving mass.

Learn how to calculate the mass of a bottle filled with water using equations. Solve the problem step-by-step with detailed explanations. Understand concepts of mass calculation and linear equations. Suitable for Grades 7-9 students.

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