there were 400 tickets for a play. 258 adult tickets at 255 each. 57 senior citizen tickets were sold at 125 each. some were sold at 150 each and the remaining were given free to the performers, friends and relatives. if 758 were collected from the sale of the tickets. how many tickets were given.
It would help if you proofread your questions before you posted them.
How many were solid at "150 each"?
How can only "758 were collected," when just "258 adult tickets at 255 each" = 65,790?
To solve this problem, let's break it down step-by-step:
Step 1: Find the total amount collected from the sale of adult tickets.
The number of adult tickets sold is 258, and the cost per ticket is $255.
So, the total amount collected from adult ticket sales is 258 * $255 = $65,790.
Step 2: Find the total amount collected from the sale of senior citizen tickets.
The number of senior citizen tickets sold is 57, and the cost per ticket is $125.
So, the total amount collected from senior citizen ticket sales is 57 * $125 = $7,125.
Step 3: Find the total amount collected from the sale of the remaining tickets.
We know that the total amount collected from all ticket sales is $758.
So, the total amount collected from the remaining tickets (including those sold at $150 and the ones given for free) can be calculated by subtracting the amount collected from adult and senior citizen tickets from the total amount collected:
Total amount collected = Amount collected from adult tickets + Amount collected from senior citizen tickets + Amount collected from remaining tickets
$758 = $65,790 + $7,125 + Amount collected from remaining tickets
Amount collected from remaining tickets = $758 - ($65,790 + $7,125)
Amount collected from remaining tickets = $758 - $72,915
Amount collected from remaining tickets = -$72,157
Step 4: Calculate the cost of the remaining tickets.
The negative value obtained in step 3 (-$72,157) indicates that the total amount collected from the remaining tickets was not enough to cover their costs. This means that the cost of the remaining tickets is greater than the amount collected, and all of these remaining tickets were given away for free.
Step 5: Calculate the number of tickets given away.
To find the number of tickets given away, we need to calculate the difference between the total number of tickets and the sum of the tickets sold.
Total number of tickets = 400
Total number of tickets sold = 258 adult tickets + 57 senior citizen tickets = 315 tickets
Number of tickets given away = Total number of tickets - Total number of tickets sold
Number of tickets given away = 400 - 315
Number of tickets given away = 85 tickets
Therefore, 85 tickets were given away for free to the performers, friends, and relatives.
To find the number of tickets that were given for free, we first need to calculate the total amount collected from the sale of adult and senior citizen tickets.
Number of adult tickets sold = 258
Price of each adult ticket = $255
Total amount collected from adult ticket sales = 258 * $255 = $65,790
Number of senior citizen tickets sold = 57
Price of each senior citizen ticket = $125
Total amount collected from senior citizen ticket sales = 57 * $125 = $7,125
Total amount collected from adult and senior citizen ticket sales = $65,790 + $7,125 = $72,915
We are told that the total collected amount from the ticket sales was $758. So, the remaining $758 - $72,915 = -$72,157 was collected from the sale of the tickets sold at $150 each and the tickets that were given for free.
Since the remaining amount is negative, it means that the total collected amount is less than the actual amount collected. This indicates that more tickets were given for free. Therefore, we cannot accurately determine the number of tickets given for free from the information provided in the question.