Lakewood High School is taking 250 students on a field trip to the natural science museum downtown. The school can use buses that seat 60 students each and vans that seat 8 students each.

Question

Which pairs (b,v) represent possible numbers of buses and vans the school can use to take the students to the museum?

3,9

3,8

2,16

0,30

Answer 1

The total number of students going on the field trip is 250.

Let's start by finding the maximum number of students that can fit on buses and vans:
Maximum number of students on buses = 60 x 3 = 180
Maximum number of students on vans = 8 x 9 = 72
Total maximum number of students = 180 (buses) + 72 (vans) = 252

Since the total number of students is 250, the school cannot use 3 buses and 9 vans.

Let's check the other options:
2 buses and 16 vans = 60 (students) x 2 (buses) + 8 (students) x 16 (vans) = 120 + 128 = 248, which is less than 250.

0 buses and 30 vans = 0 (students) x 0 (buses) + 8 (students) x 30 (vans) = 0 + 240 = 240, also less than 250.

Therefore, the only pair that represents a possible number of buses and vans is (2,16).