Question

An auditorium hold at most 740 people. The balcony holds 60 people and there are 20 rows on the main floor. Each row has the same number of seats. Ryan inequality to find how many seats there are in each row on the main floor.

Answer 1

The inequality can be given as:

`20x+60\leq740`

where
`x` represents number of seats in each row of the main floor

Each row has 34 seats.

Explanation:

Given:

The auditorium can hold at most 740 people.

The balcony holds a maximum of 60 people.

Total number of rows in the main floor = 20

Each row in main floor has same number of seats.

To write an equation to find how many seats there are in each row on the main floor

Solution:

Let the total number of seats in each row of the main floor be =
`x`

Using unitary method.

If each row has
`x` seats

Then, 20 rows will have a total of =
`20x` seats

Balcony can have a total of 60 people.

So, maximum number of people the auditorium can hold can be given as:

⇒
`20x+60`

The auditorium holds at most 740 people

Thus, the inequality can be given as:

`20x+60\leq740`

Solving for
`x` :

Subtracting both sides by 60.

`20x+60-60\leq 740-60`

`20x\leq 680`

Dividing both sides by 20.

`(20x)/(20)\leq (680)/(20)`

`x\leq 34`

This means each row can hold at most of 34 people.

Thus, each row must have = 34 seats