Question

A) Write a linear system to model the situation:

For the school play, the cost of one adult ticket is $6 and the cost of one student ticket is $4. Twice as many student tickets as adult tickets were sold. The total receipts were $2016.

b) Use substitution to solve the related problem:
How many of each type of ticket were sold?​

Answer 1

There were 126 student tickets sold and 252 adult ticket sold.

Explanation:

Let x be the number of adult tickets sold

y be the number of students tickets sold

Twice as many student tickets as adult tickets were sold

a.

x = 2y ---equation 1

6x + 4y = 2016 ---equation 2

b.

Substitute equation 1 to equation 2

6(2y) + 4y = 2016

12y + 4y = 2016

16y = 2016

Divide both sides of the equation by 16

16y/16 = 2016/16

y = 126

Substitute y = 126 to equation 1

x = 2y

x = 2(126)

x = 252