A water bottle is 7/8 full. When 1 1/2 litre water is drawn from it,it is 1/24 full. Find the capacity of the bottle in millilitres.

Let's find the total capacity of the bottle step by step.

### Step 1: Define Variables
Let \( C \) be the total capacity of the bottle in litres.

### Step 2: Calculate Initial Amount of Water
Initially, the bottle is \( \frac{7}{8} \) full, so the initial amount of water in the bottle is:

\[
\text{Initial water} = \frac{7}{8}C
\]

### Step 3: Calculate Remaining Water After Drawing
When \( 1 \frac{1}{2} \) litres (which is \( \frac{3}{2} \) litres) of water is drawn, the remaining water is:

\[
\text{Remaining water} = \frac{7}{8}C - \frac{3}{2}
\]

This remaining water makes the bottle \( \frac{1}{24} \) full.

### Step 4: Set Up the Equation
Since the remaining water is \( \frac{1}{24} \) of the total capacity, we set up the equation:

\[
\frac{7}{8}C - \frac{3}{2} = \frac{1}{24}C
\]

### Step 5: Solve for \( C \)
Multiply both sides by 24 to clear the fractions:

\[
24 \left(\frac{7}{8}C - \frac{3}{2}\right) = C
\]

Simplify the expression inside the parentheses:

\[
24 \times \frac{7}{8}C - 24 \times \frac{3}{2} = C
\]

\[
21C - 36 = C
\]

Move all terms involving \( C \) to one side:

\[
21C - C = 36
\]

\[
20C = 36
\]

\[
C = \frac{36}{20} = 1.8 \text{ litres}
\]

### Step 6: Convert Capacity to Millilitres
Since 1 litre = 1000 millilitres:

\[
C = 1.8 \times 1000 = 1800 \text{ millilitres}
\]

### Final Answer
The capacity of the bottle is **1800 millilitres**.

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Would you like to see more details, or do you have any questions?

Here are 5 related questions to explore:
1. What fraction of the bottle is left if 1 litre of water is drawn from it?
2. How would the problem change if the bottle was 3/4 full instead?
3. What would be the capacity if the remaining water was \( \frac{1}{12} \) full?
4. How much water needs to be drawn for the bottle to be half full?
5. How can you convert between different units of volume, like litres to gallons?

**Tip:** Always double-check unit conversions to avoid errors, especially when switching between litres and millilitres!

A water bottle is 7/8 full. When 1 1/2 litre water is drawn from it, it is 1/24 full. Find the capacity of the bottle in millilitres.

This problem involves calculating the total capacity of a water bottle that is 7/8 full, with 1.5 litres of water drawn from it, leaving it 1/24 full. Learn step-by-step how to solve this using algebra and fractions. Suitable for students in Grades 6-8.

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