To determine the total number of soda cans in the four partially filled cases, we need to calculate the number of cans in each case based on the given fractions of fullness and then sum them up. Here are the steps:
1. Determine the number of cans in each partially filled case:
- A full case contains 24 cans.
- The first case is [tex]\(\frac{1}{2}\)[/tex] full:
[tex]\[
\text{Cans in Case 1} = 24 \times \frac{1}{2} = 12 \text{ cans}
\][/tex]
- The second case is [tex]\(\frac{2}{3}\)[/tex] full:
[tex]\[
\text{Cans in Case 2} = 24 \times \frac{2}{3} = 16 \text{ cans}
\][/tex]
- The third case is [tex]\(\frac{5}{6}\)[/tex] full:
[tex]\[
\text{Cans in Case 3} = 24 \times \frac{5}{6} = 20 \text{ cans}
\][/tex]
- The fourth case is also [tex]\(\frac{5}{6}\)[/tex] full:
[tex]\[
\text{Cans in Case 4} = 24 \times \frac{5}{6} = 20 \text{ cans}
\][/tex]
2. Sum the number of cans from all the partially filled cases:
[tex]\[
\text{Total cans} = 12 \text{ cans} + 16 \text{ cans} + 20 \text{ cans} + 20 \text{ cans}
\][/tex]
[tex]\[
\text{Total cans} = 68 \text{ cans}
\][/tex]
Therefore, the total number of soda cans in the four partially filled cases is 68 cans.
