Answer:
2500 student tickets
500 non-student tickets.
Step-by-step explanation:
Let's call x the number of student tickets and y the number of non-student tickets.
Now, if the income was $10,000, the price of a student ticket was $3, and the price of the non-student ticket was $5 we can write the following equation:
3x + 5y = 10,000
Because 3x is the income for the student tickets and 5y is the income for the non-student tickets.
In the same way, if 3,000 tickets were sold, we can write the following equation:
x + y = 3000
Now, we need to solve the system of equations. So, solving for y, we get:
x + y - x = 3000 - x
y = 3000 - x
Then, substitute y = 3000 - x on the first equation to get:
3x + 5y = 10000
3x + 5(3000 - x) = 10000
Finally, solving for x, we get:
3x + 5(3000) - 5(x) = 10000
3x + 15000 - 5x = 10000
-2x + 15000 = 10000
-2x + 15000 - 15000 = 10000 - 15000
-2x = -5000
-2x/(-2) = -5000/(-2)
x = 2500
So, the value of y is:
y = 3000 - x
y = 3000 - 2500
y = 500
Therefore, they sold 2500 student tickets and 500 non-student tickets.