William has a 26 liter glass tank. First, he wants to put some marbles in it, all of the same volume. Then, he wants to fill the tank with water until it's completely full. If he uses 85 marbles, he will have to add 20.9 liters of water.
What is the volume of each marble?
How much water is necessary if William uses
In order to solve the problem, we need to first determine the volume of each marble.
If William uses 85 marbles and has to add 20.9 liters of water, we can establish the following equation:
Volume of marbles + Volume of water = Total volume of tank
Let V represent the volume of each marble. Since there are 85 marbles, the volume of marbles is 85V.
Thus, the equation becomes:
85V + 20.9 = 26
Subtracting 20.9 from both sides gives:
85V = 5.1
Dividing both sides by 85 gives:
V = 0.06 liters
Therefore, each marble has a volume of 0.06 liters.
Now, let's calculate how much water is necessary if William uses 100 marbles.
We know that the volume of marbles is 100V (where V is the volume of each marble) and the volume of water is W.
Using the same equation as before, we have:
100V + W = 26
We only need to find the value of W.
Substituting the volume of each marble, we have:
100 * 0.06 + W = 26
6 + W = 26
W = 26 - 6
W = 20
Therefore, if William uses 100 marbles, he will need 20 liters of water.