Question

A traveling puppet show sold 900 tickets for a certain performance. If front row tickets sold $3 each and back row tickets for $2 each, and if the total sales were $2300, how many of each kind of ticket were sold?

Answer 1

Answer: 500 front row tickets and 400 back row tickets were sold.

Step-by-step explanation:

Let x represent the number of front row tickets that were sold.

Let y represent the number of back row tickets that were sold.

A traveling puppet show sold 900 tickets for a certain performance. It means that

x + y = 900

If front row tickets sold $3 each and back row tickets for $2 each, and if the total sales were $2300, it means that

3x + 2y = 2300 - - - - - - - - - 1

Substituting x = 900 - y into equation 1, it becomes

3(900 - y) + 2y = 2300

2700 - 3y + 2y = 2300

- 3y + 2y = 2300 - 2700

- y = - 400

y = 400

Substituting y = 400 into x = 900 - y, it becomes

x = 900 - 400

x = 500