Question

A school district transported a total of 409 students and teachers to a zoo in buses and vans.

-Each bus transported a total of 55 students and teachers.
-Each van transported a total of 12 students and teachers.
-There were 5 more buses than vans.
What is the total number of students and teachers who rode to the zoo in buses? What is the total number of students and teachers who rode to the zoo in vans?

Answer 1

Explanation:

Let x be the number of buses and y be the number of vans.

We know that there are 5 more buses than vans, therefore, we can set up:

`x=y+5`

Since a bus transports 55 people and a van transports 12 people, therefore, we can set up:

`55x+12y = 409\\`

Now lets solve the above two equations together by substitution

`55(y+5)+12y = 409\\\\55y+275+12y=409\\\\67y+275=409\\\\67y=409-275\\\\67y=134\\\\y=2,x=2+5=7`

Total number of students and teachers who rode to the zoo in buses
`=55*7=385`

Total number of students and teachers who rode to the zoo in vans
`=12*2=24`