a theater has tickets at $6 for adults,$ 3.50 for students, and $2.50 for childr

Question

a theater has tickets at $6 for adults,$ 3.50 for students, and $2.50 for children under 12. a total of 278 tickets were sold for one showing with a total revenue of $1300. if the number of adult tickets sold was 10 less than twice the number of student tickets, how many of each type of ticket were sold for the showing? let x be the number of adult tickets sold, y be the number of student tickets sold, and z be the number of child tickets sold. write a system of linear equations that could be used to solve this problem.

Explanation / Answer

Solution:

Let x be the number of adults ticket sold.

y be the number of students ticket sold

and z be the number of child tickets sold

total of 278 tickets were sold

therefore x+y+z =278...........(1)

Since number of adults ticket sold was 10 less than twice the number of students ticket.

x = 2y-10 --------------(2)

According to the question

total revenue is $1300, therefore

$1300 = $6x + $3.5(y) + $2.5z--------------(3)

So (1) , (2) and (3) are the system of linear equations.

on solving these we will get the answers.

therefore,

replacing x = 2y-10 and z= 278 -(2y -10) - y

$1300 = $6(2y-10) + $3.5(y) + $2.5( 288 -3y)

or, 1300 = 12y -60 + 3.5y + 720 - 7.5y

or, 640= 8y

or, y= 80

Therefore number of adults ticket sold = 2(80)- 10 =150

number of students ticket sold= 80 and

number of child tickets sold = 278 -150-80 = 48

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