The income from a student production was $23,000. The price of a student ticket was $3, and nonstudent tickets were sold at $7 each. Five thousand tickets were sold. How many tickets of each kind were sold?
Work so far:
x = Student tickets
y = non student tickets
x + y = 23000
x = $3
y = $7
3x + 7y = 23000
Thank you.
Nope. x+y represents the total number of tickets sold. That is not 23000.
so..
3x + 7y = 50..?
No, 3x+7y = 2300 represents the total money collected. That equation is correct.
How many tickets were sold?
5,000 tickets were sold.
so, x+y=5000
So my two equations are..
x + y = 5000
3x +7y = 2300
Yes?
almost
x + y = 5000
3x +7y = 23000
Thank you very much!
To solve this problem, you have correctly set up a system of equations:
x + y = 23000 -- Equation (1)
3x + 7y = 23000 -- Equation (2)
From Equation (1), you can express x in terms of y by subtracting y from both sides:
x = 23000 - y
Now, substitute this expression for x in Equation (2):
3(23000 - y) + 7y = 23000
Distribute the 3:
69000 - 3y + 7y = 23000
Combine like terms:
4y = 46000
Divide both sides by 4:
y = 11500
Now, substitute the value of y back into Equation (1) to solve for x:
x + 11500 = 23000
x = 23000 - 11500
x = 11500
Therefore, the solution to the system of equations is x = 11500 and y = 11500. This means that 11500 student tickets and 11500 non-student tickets were sold.