Let's solve this problem step by step.
First, we need to convert the mixed numbers into improper fractions or decimal form to make calculations easier.
1. Convert [tex]\(1 \frac{1}{3}\)[/tex] cups of milk to a decimal form.
[tex]\[
1 \frac{1}{3} = 1 + \frac{1}{3} = 1 + 0.3333 \approx 1.3333
\][/tex]
2. Convert the total soup amount [tex]\(2 \frac{5}{8}\)[/tex] to a decimal form.
[tex]\[
2 \frac{5}{8} = 2 + \frac{5}{8} = 2 + 0.625 = 2.625
\][/tex]
3. Determine the amount of condensed soup.
The total amount of soup is the sum of the milk and the condensed soup. To find out how much condensed soup Alan used, we subtract the amount of milk from the total soup:
[tex]\[
\text{Condensed Soup} = \text{Total Soup} - \text{Milk}
\][/tex]
Substituting the values we converted:
[tex]\[
\text{Condensed Soup} = 2.625 - 1.3333 = 1.2917
\][/tex]
4. Compare the result with the given options.
We need to identify which of the given options matches [tex]\(1.2917\)[/tex]:
[tex]\[
1 \frac{7}{24} \approx 1.2917
\][/tex]
[tex]\[
1 \frac{1}{6} \approx 1.1667
\][/tex]
[tex]\[
3 \frac{23}{24} \approx 3.9583
\][/tex]
[tex]\[
1 \frac{4}{5} \approx 1.8000
\][/tex]
Among these options, [tex]\(1 \frac{7}{24}\)[/tex] is approximately equal to [tex]\(1.2917\)[/tex].
Therefore, the amount of condensed soup in the can is [tex]\( \boxed{1 \frac{7}{24}} \)[/tex].
