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

Answer:

The number of students a van can carry  is 10 students

Number of students a bus can carry is  25 students

Step-by-step 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