Grant Valley School has hired a fleet of buses and vans to transport 96 students to a picnic. Each bus can seat 31 people, and each van can seat 9 people. The school authorities want to have three teachers traveling in each bus and one teacher in each van.
It will take
to accommodate 107 people, including the students and teachers, with no seats left vacant.

Question

Grant Valley School has hired a fleet of buses and vans to transport 96 students to a picnic. Each bus can seat 31 people, and each van can seat 9 people. The school authorities want to have three teachers traveling in each bus and one teacher in each van.
It will take 
to accommodate 107 people, including the students and teachers, with no seats left vacant.

jhonyy9 · Answer

what is the question here ?

Extrinix · Answer

@jhonyy9 wrote:

what is the question here ?

It’s asking how many buses and vans will it take to accommodate 107 people, leaving no spaces open

Extrinix · Answer

I’m thinking something like this?

$\sf{107 = 31(x) + 9(y)}$

Where $\sf{x}$ equals the amount of buses and $\sf{y}$ equals the amount of vans.

Am I looking at this correct, @jhonyy9 ?

jhonyy9 · Answer

yes but there is a second equation too

jhonyy9 · Answer

,, The school authorities want to have three teachers traveling in each bus and one teacher in each van."

Extrinix · Answer

Ah so $\sf{107 = 31(3 + x) + 9(1 + y)}$?

Extrinix · Answer

No because that would be different, I need to swap out the variable placements

$\sf{96 = x(31-3)+y(9-1)}$

That’s what I’m thinking… ?

jhonyy9 · Answer

@extrinix wrote:

Ah so $\sf{107 = 31(3 + x) + 9(1 + y)}$?

I think this 31 will be 28+3 and this 9 will be 8+1

Extrinix · Answer

@jhonyy9 wrote:

@extrinix wrote:

Ah so $\sf{107 = 31(3 + x) + 9(1 + y)}$?

I think this 31 will be 28+3 and this 9 will be 8+1

I corrected myself because 107 is the total amount (students and teachers), so we could just remove the amount of teachers from the equation and from the total slots on each vehicle type

Extrinix · Answer

That’s where this equation came from $\sf{\downarrow}$ $\sf{\downarrow}$

@extrinix wrote:

No because that would be different, I need to swap out the variable placements $\sf{96 = x(31-3)+y(9-1)}$ That’s what I’m thinking… ?

jhonyy9 · Answer

this 31 = 28 students + 3 teachers in a bus 
and 9 = 8 students +1 teacher in a van

surjithayer · Answer

96+3x+y=107
3x+y=107-96=11
31x+9y=107
31x+9(11-3x)=107
31x+99-27x=107
4x=107-99=8
x=8/4=2
2(3)+y=11
y=11-6=5
number of buses=2
number of vans=5

surjithayer · Answer

here number of buses=x
number of vans=y