Answer:
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
