Question

The senior classes at High School A and High School B planned separate trips to the water park. The senior class at High School A rented and filled 14 vans and 2 buses with 270 students. High School B rented and filled 9 vans and 9 buses with 459 students. Each van and each bus carried the same number of students. Find the number of students in each van and in each bus.

Answer 1

x = number of students in the van = 14

y = number of students in the bus = 37

Explanation:

Let

x = number of students in the van

y = number of students in the bus

14x + 2y = 270 (1)

9x + 9y = 459 (2)

Multiply (1) by 9 and (2) by 2

126x + 18y = 2,430 (3)

18x + 18y = 918 (4)

Subtract (4) from (3)

126x - 18x = 2,430 - 918

108x = 1,512

x = 1,512 / 108

= 14

x = 14 students in each van

Substitute x = 14 into (1)

14x + 2y = 270

14(14) + 2y = 270

196 + 2y = 270

2y = 270 - 196

2y = 74

y = 74/2

= 37

y = 37 students in each bus

x = number of students in the van = 14

y = number of students in the bus = 37