Question

Two schools went on a field trip. School A needed six busses and two

vans to take 162 students. School B needed four busses and four vans to
take 132 students. How many students rode on each bus and each van?
3

Answer 1

• bus: 24
• van: 9

Explanation:

You want to know the number of students who rode in each bus and van when 6 buses and 2 vans can hold 162 students, while 4 buses and 4 vans can hold 132 students.

Setup

We can write these equations for the numbers of students transported:

6b +2v = 162

4b +4v = 132

Solution

Subtracting half the second equation from the first, we have ...

(6b +2v) -1/2(4b +4v) = (162) -1/2(132)

4b = 96 . . . . . simplify

b = 24 . . . . . divide by 4

Using this value in the second equation, we have ...

96 +4v = 132

4v = 36 . . . . . . . subtract 96

v = 9 . . . . . . divide by 4

24 students rode on each bus; 9 students rode in each van.

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