Question

The local Orchestra has been invited to play at a festival. There are 111 members of the orchestra and six are licensed to drive large multiple passenger vehicles. Busses 25 people but are much more expensive to rent passenger vans for 12 people. Create a system of equations to find the small list number of buses there orchestra can rent.

Answer 1

Small list number of buses
`=3`,the orchestra can rent.

Explanation:

Form an equation representing the number of vehicles needed.

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

We have six drivers so,

`x + y\leq 6` for both vehicles.

And it's an inequality,where we can equate with by removing the inequality to close in our answer.

`x + y = 6`

Then form an equation representing the total number of seats
`K` in vehicles for the orchestra members.

`25` people for bus and
`12` people for vans can be written in terms of seats.

So,
`K = 25x + 12y`

In terms of an inequality it can be written as,

`25x + 12y\geq111`,
`111` is the maximum numbers of the orchestra.

Solving the system of inequality.

We have

`x + y = 6`

Re-arranging y.

`y = 6 - x`

Plugging the values in
`25x + 12y\geq111` by removing the inequality and considering it as an equation.

`111 = 25x + 12y = 25x + 12(6-x)`

`111 = 25x + 72 - 12x`

`111 - 72 = 13 x`

`39 = 13 x`

`x = 3`

So small list number of buses are
`3` there orchestra can rent.