The school production of 'Our Town' was a big success. For opening night, 315 tickets were sold. Students paid $1.50 each, while non-students paid $3.50 each. If a total of $ 686.50 was collected, how many students and how many non-students attended?

There are 208 student and 107 non-student

Step-by-step explanation:

* Lets change the story problem to equations and solve them

- In the opening night 315 ticket were sold

- Each student paid $1.50 for a ticket

- Non-student paid $3.50 for a ticket

- The total money collected this night was $686.50

- Lets consider the number of student's ticket is x and the number

of non-student's ticket is y

∵ The total number of the tickets is 315 tickets

∴ x + y = 315 ⇒ (1)

∵ The total amount of money is $686.50

∵ The cost of the student's ticket is $1.50

∵ The cost of the non-student's ticket is $3.50

∴ 1.50x + 3.50y = 686.50 ⇒ (2)

* Lets solve the two equation to find x and y by substitution method

- From equation (1) find x in term of y

∵ x + y = 315 ⇒ subtract y from both sides

∴ x = 315 - y ⇒ (3)

- Substitute x in equation (2) by equation (3)

∴ 1.50 (315 - y) + 3.50y = 686.50 ⇒ open the bracket

∴ 472.50 - 1.50y + 3.50y = 686.50 ⇒ add the like terms

∴ 472.50 + 2y = 686.50 ⇒ subtract 472.50 from both sides

∴ 2y = 214 ⇒ divide both sides by 2

∴ y = 107

- Substitute the value of y in equation (1)

∴ x + 107 = 315 ⇒ subtract both sides by 107

∴ x = 208

∵ x represents the number of student's tickets and y represents

the number of non-student's ticket

∴ There are 208 student and 107 non-student