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.
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
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).