There were 1000 more students at the soccer game than nonstudents. Student tickets were $8.50 and nonstudent tickets were $13.25. If the total revenue for the game was $75,925, then how many tickets of each type were sold?
Wrte two equations in the two unknowns S (student tickets sold) and N (nonstudent tickets sold).
S + N = 1000
8.5 S + 13.25 N = 75,925.
Now solve for N and S using elimination or substitution.
To solve this problem, we can use a system of equations to represent the given information.
Let's assume the number of nonstudent tickets sold is x.
Then the number of student tickets sold would be x + 1000 because there were 1000 more students at the game than nonstudents.
The revenue from nonstudent tickets can be calculated as the price of each nonstudent ticket, $13.25, multiplied by the number of nonstudent tickets sold, which is x.
Similarly, the revenue from student tickets can be calculated as the price of each student ticket, $8.50, multiplied by the number of student tickets sold, which is x + 1000.
According to the problem, the total revenue from both types of tickets is $75,925. So we can write the equation:
13.25x + 8.5(x + 1000) = 75,925
Now we can solve this equation to find the value of x, which represents the number of nonstudent tickets sold.
13.25x + 8.5x + 8,500 = 75,925
21.75x + 8,500 = 75,925
21.75x = 67,425
x ≈ 3,100
Hence, approximately 3,100 nonstudent tickets were sold. We can also find the number of student tickets sold by adding 1000 to this value:
x + 1000 ≈ 3,100 + 1000 ≈ 4,100
Therefore, approximately 4,100 student tickets were sold.
In conclusion, approximately 3,100 nonstudent tickets and 4,100 student tickets were sold for the soccer game.