To find the volume of each marble and determine how much water is necessary if William uses 200 marbles, we start with the information provided.
- Total volume of the tank: 26 liters
- Number of marbles used: 85 marbles
- Volume of water when using 85 marbles: 20.9 liters
Let's denote the volume of each marble as \( v \) liters.
When William fills the tank with 85 marbles, the total volume occupied by the marbles is \( 85v \) liters. The remaining volume in the tank is occupied by water.
The equation representing the total volume of the tank is:
\[ \text{Volume of marbles} + \text{Volume of water} = \text{Total volume of tank} \]
This can be expressed mathematically as:
\[ 85v + 20.9 = 26 \]
Now we'll solve for \( v \):
- Rearranging the equation:
\[ 85v = 26 - 20.9 \]
Calculating the right side:
\[ 26 - 20.9 = 5.1 \]
So we have:
\[ 85v = 5.1 \]
Now we solve for \( v \):
\[ v = \frac{5.1}{85} \approx 0.06 \text{ liters} \]
This means the volume of each marble is approximately \( 0.06 \) liters.
Next, we determine how much water is necessary if William uses 200 marbles.
- Calculate the total volume occupied by 200 marbles:
\[ \text{Volume of marbles} = 200v = 200 \times 0.06 = 12 \text{ liters} \]
- Now, calculate the volume of water required:
The remaining volume in the tank can be calculated as:
\[ \text{Volume of water} = 26 - \text{Volume of marbles} \]
So,
\[ \text{Volume of water} = 26 - 12 = 14 \text{ liters} \]
In summary:
- The volume of each marble is approximately \( 0.06 \) liters.
- If William uses 200 marbles, he will need \( 14 \) liters of water.
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