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
