The income from a student production was $15,000. The price of a student ticket was $3, and nonstudent tickets were sold at $5 each. Four thousand tickets were sold. How many tickets of each kind were sold?
s = 4000 - n
3s + 5n = 15,000
Substitute 4000-n for s.
3(4000-n) + 5n = 15,000
Solve for n, then s.
To solve this problem, let's set up a system of equations to represent the given information.
Let's assume that x represents the number of student tickets sold, and y represents the number of nonstudent tickets sold.
We know that the total number of tickets sold was 4000, so the first equation is:
x + y = 4000 (equation 1)
The second equation comes from the statement that the income from the student production was $15,000. Since the price of a student ticket was $3, and nonstudent tickets were sold at $5 each, the equation is:
3x + 5y = 15000 (equation 2)
Now we have a system of equations:
x + y = 4000 (equation 1)
3x + 5y = 15000 (equation 2)
We can solve this system of equations to find the values of x and y.
Using equation 1, we can express x in terms of y:
x = 4000 - y
Substituting this expression for x in equation 2, we get:
3(4000 - y) + 5y = 15000
Now, let's solve this equation for y.
12,000 - 3y + 5y = 15000
2y = 3000
y = 1500
Now that we have the value of y, we can substitute it back into equation 1 to find x:
x + 1500 = 4000
x = 4000 - 1500
x = 2500
Therefore, 2500 student tickets and 1500 nonstudent tickets were sold.