Two buses and a van were employed to transport a class of students on a field trip. 3/5 of the class boarded the first bus. 1/2 of the remaining students boarded the second bus, and the rest of the students boarded the van. When the second bus broke down, 1/2 of the students on the second bus boarded the first bus. What fraction of the class was on board the first bus?
Choose one.
A) a) 1/2
B) b) 7/10
C) c) 11/15
D) d) 23/30
E) e) 4/5
This is a pure ratio question (we aren't given any numbers for anything), so you can just choose any starting number you like, and use it to solve the problem. The best number to pick is almost always the product of all the denominators of your fractions, so here we could start with 30 students. Then we have:   • 3/5 of these, or 18 students, board the first bus   • there are 12 students left. 1/2 of these, or 6 students, board the second bus   • this bus breaks down, and 1/2 of the 6 students, or 3 students, board the first bus   • the first bus now contains 21 out of the original 30 students, so the answer is 21/30 = 7/10   Answer b) 7/10
<result>B</result>
Two buses and a van were employed to transport a class of students on a field trip. 3/5 of the class boarded the first bus. 1/2 of the remaining students boarded the second bus, and the rest of the students boarded the van. When the second bus broke down, 1/2 of the students on the second bus boarded the first bus. What fraction of the class was on board the first bus?