Question

The high school took two field trips to the Newport Aquarium many many years ago. They used school buses and vans to transport all the students. On the first trip there were 3 vans and two buses with 122 students. The second trip was more popular, with 5 vans and 3 buses, carrying 189 students. Use a system of equations to determine the number of students that a van and a bus can carry

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Answer 1

bus = 43

van 12

Explanation:

This can be solved using simultaneous equations

Let v represent the number of students that a van carries

Let b represent the number of students that a bus carries

the following equations can be derived from the question

3v + 2b = 122 eqn 1

5v + 3b = 189 eqn 2

Multiply eqn 1 by 5 and eqn 2 by 3

15v + 10b = 610 eqn 3

15v + 9b = 567 eqn 4

Subtract equation 4 from 3

b = 43

Substitute for b in equation 1

3v + 2(43) = 122

solve for v

v = 12