14. Adult tickets for a school fashion show cost $8 and student tickets cost $5. The total receipts for 200 tickets are $1150. Using an algebraic method (the method of substitution or elimination), determine the number of each ticket that was sold. Be sure to define the variables. (6 marks)
Let x be the number of adult tickets sold and y be the number of student tickets sold.
We can set up a system of two equations to represent the given information:
x + y = 200 (equation 1: the total number of tickets sold is 200)
8x + 5y = 1150 (equation 2: the total receipts from ticket sales is $1150)
We can use either substitution or elimination method to solve for x and y. Let's use elimination method:
Multiply equation 1 by 5 to get 5x + 5y = 1000
Subtract this equation from equation 2 to eliminate y:
8x + 5y = 1150
- (5x + 5y = 1000)
-----------------------
3x = 150
So, x = 50. This means 50 adult tickets were sold. Substituting this value into equation 1, we can find y:
50 + y = 200
y = 150
Therefore, 150 student tickets were sold.
Answer: 50 adult tickets and 150 student tickets were sold.