Final answer:
30 more adult tickets were sold than student tickets. A total of $720 in adult ticket sales was collected.
Step-by-step explanation:
To determine how many more adult tickets than student tickets were sold for the school play and the total sales in adult ticket sales, let's define two variables:
- x for the number of adult tickets
- y for the number of student tickets
Given the following two equations based on the problem statement:
- x + y = 150 (the total number of tickets sold)
- 8x + 5y = 1020 (the total sales from the tickets)
We can solve this system of equations using the substitution or elimination method. For simplicity, we'll use the elimination method:
Multiply the first equation by 5 to align the coefficients of y:
- 5x + 5y = 750
- 8x + 5y = 1020
By subtracting the first new equation from the second equation, we eliminate y:
- (8x + 5y) - (5x + 5y) = 1020 - 750
- 3x = 270
- x = 90 (number of adult tickets sold)
Substitute the value of x into the first original equation:
90 + y = 150
y = 150 - 90
y = 60 (number of student tickets sold)
Now we know that 90 adult tickets and 60 student tickets have been sold. To find out how many more adult tickets than student tickets were sold:
90 - 60 = 30
So, 30 more adult tickets were sold than student tickets.
To find out the total money in adult ticket sales:
90 (number of adult tickets) x 8 (cost per adult ticket) = $720
Therefore, $720 in adult ticket sales was collected.