A movie theater sold a total of 520 adult and child tickets on a certain day. The theater sold 2.25 times as many adult tickets as child tickets. Each adult ticket cost $9 and each child ticket cost $2. How much revenue did the theater generate in ticket sales that day?
For every child ticket, 2.25 adult tickets were sold.
This is the same as
For every 4 child tickets sold, 9 adult tickets were sold, for a total of 4*2+9*9=$89.
Number of sets of sets (4+9) sold = 520/13=40
Total amount = 40*$89=$3560
Alternatively, using algebra,
A=number of adult tickets sold, then
A/2.25 = number of child tickets sold.
Therefore
A+A/2.25=520
A=520/(1+1/2.25)=520*(2.25/3.25)=360
Number of child tickets sold = 520-350= 160
Total revenue
=360*9+160*2
=3240+320
=$3560
Let's first assume that the number of child tickets sold is x.
Since the theater sold 2.25 times as many adult tickets as child tickets, the number of adult tickets sold would be 2.25x.
Therefore, the total number of tickets sold is x + 2.25x = 3.25x.
We know that the total number of tickets sold is 520, so we can write the equation 3.25x = 520.
To solve for x, divide both sides of the equation by 3.25:
x = 520 / 3.25 = 160.
Now that we have the number of child tickets, we can find the number of adult tickets sold:
Number of adult tickets = 2.25x = 2.25 * 160 = 360.
To find the revenue generated from adult tickets, multiply the number of adult tickets by the cost per adult ticket:
Revenue from adult tickets = 360 * $9.
To find the revenue generated from child tickets, multiply the number of child tickets by the cost per child ticket:
Revenue from child tickets = 160 * $2.
Adding the revenue from adult and child tickets gives the total revenue generated by the theater:
Total revenue = Revenue from adult tickets + Revenue from child tickets.
To find the revenue generated by the theater in ticket sales, you first need to determine the number of adult and child tickets sold.
Let's assume the number of child tickets sold is x. Since the theater sold 2.25 times as many adult tickets as child tickets, the number of adult tickets sold would be 2.25x.
The total number of tickets sold is given as 520. So, we can set up an equation:
x + 2.25x = 520
Combining like terms, we get:
3.25x = 520
To solve for x, we divide both sides of the equation by 3.25:
x = 520 / 3.25
x ≈ 160
So, approximately 160 child tickets were sold. Since the number of adult tickets sold is 2.25 times the number of child tickets, the number of adult tickets sold can be calculated as:
2.25 * 160 ≈ 360
Now that we have the number of adult and child tickets sold, we can calculate the revenue generated by multiplying the number of tickets by their respective prices.
Revenue from adult tickets: 360 tickets * $9 per ticket = $<<360*9=3240>>3240
Revenue from child tickets: 160 tickets * $2 per ticket = $<<160*2=320>>320
Adding the revenue from adult and child tickets together:
Total revenue = $3240 + $320 = $<<3240+320=3560>>3560
Therefore, the theater generated a total revenue of $3560 in ticket sales that day.