Question

Senior classes at High School A and High School B planned separate trips to Six Flags for

their senior trip this year. High School A had a total of 350 students who rented and filled
5 vans and 12 buses. High School B had a total of 250 students who rented and filled 10
vans and 6 buses. Every van had the same number of students, as did the buses. How
many students can the van carry? How many students can the van carry?

Answer 1

The number of students a van can carry is 10 students

Number of students a bus can carry is 25 students

Explanation:

Let the number of students in each van = x

and Let the number of students in each bus = y

Now, for High School A

Total students who went on trip = 350

Number of students in 5 vans = 5 times (number of students in each van)

= 5(x) = 5 x

Number of students in 12 buses = 12 times (number of students in each bus)

= 12(y) = 12 y

⇒5x + 12y = 350

For High School B

Total students who went on trip = 250

Number of students in 10 vans = 10 times (number of students in each van)

= 10(x) = 10 x

Number of students in 6 buses = 6 times (number of students in each bus)

= 6(y) = 6 y

⇒10 x + 6 y = 250

Now, the given system of equation are:

5x + 12y = 350 ........ (1)

10 x + 6 y = 250 ........ (2)

Multiply eq (1) with -2 and add with (2), we get

-10x -24 y + 10x + 6y = -700 + 250

or, -18 y = -450

or, y = 450/18 = 25 ⇒ y = 25

putting the value of y in (1), we get x = 10

Hence, the number of students a van can carry = x = 10 students

and the number of students a bus can carry = y = 25 students