Question

2.11 A concert is performed for a crowd of 118

people. Adult tickets cost $20 each, student tickets
cost $16 each, and children tickets cost $11.50 each.
The revenue for the concert is $1745.00. There are
40 more children at the concert than students. How
many of each type of ticket are sold?

Answer 1

Number of Students who attended = 22

Number of Adults who attended = 34

Number of Children who attended = 62

Explanation:

Total crowd at concert = 118

Cost of each adult's ticket = $20

Cost of each student's ticket = $16

Cost of each children's ticket = $11.50

The total revenue of the concert = $1745.00

Now, Let the number of students = k

So, the number of children = k + 40

So, number of adults = 118 - {k + (k + 40)}

= 118- 2k -40 = 78 -2k

So, the total revenue = Total revenue from {adults + students + children}

or, $1745.00 = (78 -2k)(20) + k(16) +(k+40)(11.50)

here, solving for the value of k :

12.5k = 2020 - 1745

or k = 275\12.5 = 22

So, the Number of students who attended = 22

Number of Adults who attended = 78 - 2k = 78 - 44 = 34

Number of children who attended = k + 40 = 22 + 40 = 62