Question

The senior classes at High School A and High School B planned separate trips to Lake Compounce. The senior class at High School A rented and filled 6 vans and 7 buses with 412 students. High school B rented and filled 6 vans and 9 buses with 504 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.

Answer 1

Number of students in vans =15 and bus =46

Explanation:

use variables for the vans and buses

let x= vans and y=buses

Now solve the 2 equations simultaneously

remember to number your equations

6x+7y=412..........1

6x+9y=504.........2

make x the subject of one equation

and label it equation 3

6x=412—7y

`x = (206)/(3) - (7y)/(6) .............3`

subs 3 into 2

`6( (206)/(3) - (7y)/(6) ) + 9y = 504`

`412 - 7y + 9y = 504`

`- 7y + 9y = 504 - 412`

`2y = 92`

`y = 46...................4`

subs 4 into 1

`6x + 7(46) = 412`

`6x + 322 = 412`

`6x = 412 - 322`

`6x = 90`

`x = 15`

Therefore there are 15 students in each van and 46 students in each bus.