To solve this problem step by step, we need to find out the number of adults who went on the field trip with the fifth-grade classes given the provided conditions.
1. Determine the total number of seats filled on the four fully occupied buses:
Each bus has 40 seats, and all seats on four buses were filled.
[tex]\[
\text{Seats filled on four fully occupied buses} = 4 \times 40 = 160
\][/tex]
2. Calculate the number of seats filled on the fifth bus:
The problem states that [tex]\(\frac{4}{5}\)[/tex] of the seats on the fifth bus were filled. Since each bus has 40 seats:
[tex]\[
\text{Seats filled on the fifth bus} = \frac{4}{5} \times 40 = 32
\][/tex]
3. Total number of seats filled on all five buses:
To get the total number of seats filled, add the seats filled on the four fully occupied buses and the seats filled on the fifth bus.
[tex]\[
\text{Total seats filled} = 160 + 32 = 192
\][/tex]
4. Determine the number of adults:
According to the problem, [tex]\(\frac{1}{8}\)[/tex] of all the passengers were adults.
[tex]\[
\text{Number of adults} = \frac{1}{8} \times 192 = 24
\][/tex]
Therefore, the number of adults who went on the field trip with the fifth-grade classes is:
[tex]\[
\boxed{24}
\][/tex]
