A movie theater sold a total of 390 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 $8 and each child ticket cost $3. How much revenue did the theater generate in ticket sales that day?
To find the revenue generated by the theater, we need to determine the number of adult and child tickets sold separately.
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 390, so we can create an equation:
x + 2.25x = 390
Combining like terms, we have:
3.25x = 390
Now, let's solve for x by dividing both sides of the equation by 3.25:
x = 390 / 3.25
x = 120
Therefore, the number of child tickets sold is 120.
Now, let's calculate the revenue generated by adult tickets. Each adult ticket costs $8, and the number of adult tickets sold is 2.25x:
Revenue from adult tickets = $8 * 2.25x
Revenue from adult tickets = $8 * 2.25 * 120
Revenue from adult tickets = $2160
Similarly, we can calculate the revenue generated by child tickets. Each child ticket costs $3, and the number of child tickets sold is x:
Revenue from child tickets = $3 * x
Revenue from child tickets = $3 * 120
Revenue from child tickets = $360
Finally, to find the total revenue generated by ticket sales, we add the revenue from adult and child tickets:
Total revenue = Revenue from adult tickets + Revenue from child tickets
Total revenue = $2160 + $360
Total revenue = $2520
Therefore, the theater generated $2520 in ticket sales that day.
Let's solve the problem step-by-step.
Step 1: Let's represent the number of child tickets as "x".
Therefore, the number of adult tickets sold would be 2.25 times that of child tickets, so it would be 2.25x.
Step 2: The total number of tickets sold is given as 390.
So, we have the equation: x + 2.25x = 390
Step 3: Simplify the equation:
3.25x = 390
Step 4: Solve for x by dividing both sides of the equation by 3.25:
x = 390 / 3.25
x ≈ 120
Step 5: Now that we have found the number of child tickets, we can find the number of adult tickets:
2.25x ≈ 2.25 * 120
≈ 270
Step 6: To find the revenue generated, we multiply the number of child tickets by the cost of each child ticket and the number of adult tickets by the cost of each adult ticket, then add the two amounts together:
Revenue = (number of child tickets * cost per child ticket) + (number of adult tickets * cost per adult ticket)
Revenue = (120 * $3) + (270 * $8)
Revenue ≈ $360 + $2160
Revenue ≈ $2520
Therefore, the theater generated $2520 in ticket sales that day.
a + c = 390
a = 2.25 c
so 2.25 c + 1 c = 390, solve for c then for a
Revenue = 8 a + 3 c