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The water park is a popular field trip destination. This year the senior class at High School A and
the senior class at High School B both planned trips there. The senior class at High School A
rented and filled 10 vans and 8 buses with 394 students. High School B rented and filled 5 vans
and 10 buses with 365 students. Every van had the same number of students in it as did the
buses. Find the number of students in each van and in each bus.
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Let x be the number of students per van, and
let y be the number of students per bus.
Write equations as you read the problem
10x + 8y = 394, (1)
5x + 10y = 365. (2)
Solve the system by the Elimination method.
For it, multiply equation (2) by 2 (both sides). Keep equation (1) as is
10x + 8y = 394, (1')
10x + 20y = 730. (2')
From equation (2') subtract equation (1'). You will get
20y - 8y = 730 - 394,
12y = 336
y = 436/12 = 28.
Now from equation (1) find x, substituting x = 28 there
10x + 8*28 = 394,
10x = 394 - 8*28 = 170,
x = 170/10 = 17.
ANSWER. 17 students in each van and 28 students in each bus.
Solved.