To determine how many more quarts of water the pot can hold, we need to follow a few steps. Here is the detailed solution:
1. Total Capacity Calculation:
First, convert the mixed number [tex]\(5 \frac{1}{2}\)[/tex] to an improper fraction or a decimal.
[tex]\[
5 \frac{1}{2} = 5 + \frac{1}{2} = 5.5 \text{ quarts}
\][/tex]
So, the total capacity of the pot is 5.5 quarts.
2. Fraction of the Pot Filled:
We are given that the pot is [tex]\(\frac{2}{3}\)[/tex] filled with water.
[tex]\[
\text{Filled fraction} = \frac{2}{3}
\][/tex]
3. Calculate the Amount of Water in the Pot:
Multiply the total capacity by the fraction that is filled to find out how much water is currently in the pot.
[tex]\[
\text{Filled amount} = 5.5 \times \frac{2}{3}
\][/tex]
This calculation gives:
[tex]\[
\text{Filled amount} \approx 3.6667 \text{ quarts}
\][/tex]
4. Calculate the Remaining Capacity:
Subtract the filled amount from the total capacity to find out how much more water the pot can hold.
[tex]\[
\text{Remaining capacity} = 5.5 - 3.6667
\][/tex]
This calculation gives:
[tex]\[
\text{Remaining capacity} \approx 1.8333 \text{ quarts}
\][/tex]
So, the pot can hold approximately 1.8333 more quarts of water.
