Question

There are 5 sections of reserved seating and 8 sections of general seating for a concert. Each section has 30 seats. A head count revealed that the concert was at 80 percent capacity. The concert hall regulations call for 1 security guard for every 50 people in attendance. How many people are at the concert?How many security guards need to be on duty at the concert

Answer 1

There were 312 people at the concert.

7 security guards were needed on duty at the concert.

Explanation:

Given:

Number of sections of reserved seating = 5

Number of sections of general seating = 8

Number of seats in each section = 30

We need to find the number of people in the concert and number of security guards need to be on duty at the concert.

Solution:

first we we will find the capacity of the concert.

capacity of the concert can be calculated by Number of sections of reserved seating multiplied by Number of seats in each section plus Number of sections of general seating multiplied by Number of seats in each section.

framing in equation form we get;

capacity of the concert =
`5* 30+8* 30= 150+240 = 390`

Now Given:

Concert was at 80% capacity.

So we can say that;

Number of people at the concert is equal to 80% of the Total capacity of the concert.

framing in equation form we get;

Number of people at the concert =
`(80)/(100)* 390 = 312`

Hence There were 312 people at the concert.

Now Given that;

50 people = 1 security guard

312 people = Number of security guards for 312 people.

using Unitary method we get;

Number of security guards for 312 people =
`(312)/(50) = 6.24`

Hence we can say that 7 security guards were needed on duty at the concert.