3/5 of a certain class left on a field trip. 1/3 of the students who stayed behind did not want to go on the field trip (all the others did want to go). When another vehicle was located, 1/2 of the students who did want to go on the field trip but had been left behind were able to join. What fraction of the class ended up going on the field trip?

11/15

Step-by-step explanation:

In this kind of problem, it is cool to always have a value for the total number of students. We can choose any arbitrary value for this. So let's say the total number of students is 120.

Now we were told 3/5 left for the field trip. The number that left corresponds to 3/5 of 120 = 72 students. The number that didn't go on the field trip is thus 120 - 72 = 48 students.

Now what do we know again? 1/3 of those who stayed behind didn't want to go. The number that didn't want to go is thus 1/3 of 48 = 16. The number that wanted to go but didn't leave with the first batch is thus 48 - 16 = 32

Now, a bus came along and half of those who wanted to go but were left behind joined. This is equal to a value of 1/2 * 32 = 16

Now the question is what fraction of the class left for the field trip. All we need do is add the first batch to the second batch and divide the result by the total number of students. The addition of both yields = 72 + 16 = 88 students.

The fraction that left was thus 88/120 = 11/15