As for the admission ticket of a certain theater, the advance tickets and the day tickets are available at a rate of 7 : 3.
The advance tickets are on sale three weeks before to the previous day and the day tickets are on sale 2 hours before opening of the performance.
The day ticket audience of one day began to stand in a line 3 hours before opening and joined the sequence four persons per one minute.
The day tickets were sold at a sales window of the theater to six persons per one minute.
Answer the following questions.
(1) How many day tickets audience had stood in a line 10 minutes before opening of the performance?
(2) How many minutes did the person take to enter the theater who is the day tickets visitor and was in the 120th from the beginning of the line?
(Find the time this person was in the line.)
(3) Before opening of the performance, ten percent of scheduled number of the advance tickets remained unsold and 80 percent of schedule number of of the day tickets were sold.
Find the total number of audience this day.
The advance tickets are on sale three weeks before to the previous day and the day tickets are on sale 2 hours before opening of the performance.
The day ticket audience of one day began to stand in a line 3 hours before opening and joined the sequence four persons per one minute.
The day tickets were sold at a sales window of the theater to six persons per one minute.
Answer the following questions.
(1) How many day tickets audience had stood in a line 10 minutes before opening of the performance?
(2) How many minutes did the person take to enter the theater who is the day tickets visitor and was in the 120th from the beginning of the line?
(Find the time this person was in the line.)
(3) Before opening of the performance, ten percent of scheduled number of the advance tickets remained unsold and 80 percent of schedule number of of the day tickets were sold.
Find the total number of audience this day.
Answer
Solution
(1) Since line up at the rate of four persons per one minute from three hours before the curtain, the number of people lined up in 2 hours 50 minutes = 170 minutes which is the time of 10 minutes before the opening, 4 persons × 170 minutes = 680 persons..
Because the day tickets are on sale 2 hours before opening, during 1 hour and 50 minutes which is the time of 10 minutes before opening the number of persons whom tickets are sold is 6 persons × 110 minutes = 660 persons.
Therefore there are 20 persons in the line 10 minutes before opening as 680 - 660 = 20.
(2) There are one hour = 60 minutes until the time of the day tickets on sale.
According to the calculation of 120 persons / four persons = 30 minutes, the 120th person was stood in the line before the time of the day tickets sale.
Since six persons enter per one from a sale start, this person needs to take 120 persons / six person = 20 minutes to enter.
Above all, the time taken the 120th person to enter is 30 minutes + 20 minutes = 50 minutes.
（3） Since the selling hours of the day tickets are 120 minutes and tickets were sold at the rate of six persons per one minute, the number of tickets sold is six sheets × 120 minutes = 720 sheets.
Since 720 sheets is equivalent to 80 percent of schedule number of sheets, schedule number of sheets is 720 / 0.8 = 900 sheets.
Since the ratio of the sales schedule number of the advance tickets and the day tickets was 7:3 and there was 900 schedule number of the day tickets, the schedule number of the advance tickets is 900 / 3 × 7 = 2100 sheets.
Since the sales number of the advance tickets was 90 percent of schedule number, it is 2100 sheets × 0.9= 1890 sheets.
Above all, the total number of audience is 720 + 1890 = 2610 persons.
(1) 20 persons
(2) 50 minutes
(3) 2610 persons
(2) 50 minutes
(3) 2610 persons
(1) Since line up at the rate of four persons per one minute from three hours before the curtain, the number of people lined up in 2 hours 50 minutes = 170 minutes which is the time of 10 minutes before the opening, 4 persons × 170 minutes = 680 persons..
Because the day tickets are on sale 2 hours before opening, during 1 hour and 50 minutes which is the time of 10 minutes before opening the number of persons whom tickets are sold is 6 persons × 110 minutes = 660 persons.
Therefore there are 20 persons in the line 10 minutes before opening as 680 - 660 = 20.
(2) There are one hour = 60 minutes until the time of the day tickets on sale.
According to the calculation of 120 persons / four persons = 30 minutes, the 120th person was stood in the line before the time of the day tickets sale.
Since six persons enter per one from a sale start, this person needs to take 120 persons / six person = 20 minutes to enter.
Above all, the time taken the 120th person to enter is 30 minutes + 20 minutes = 50 minutes.
（3） Since the selling hours of the day tickets are 120 minutes and tickets were sold at the rate of six persons per one minute, the number of tickets sold is six sheets × 120 minutes = 720 sheets.
Since 720 sheets is equivalent to 80 percent of schedule number of sheets, schedule number of sheets is 720 / 0.8 = 900 sheets.
Since the ratio of the sales schedule number of the advance tickets and the day tickets was 7:3 and there was 900 schedule number of the day tickets, the schedule number of the advance tickets is 900 / 3 × 7 = 2100 sheets.
Since the sales number of the advance tickets was 90 percent of schedule number, it is 2100 sheets × 0.9= 1890 sheets.
Above all, the total number of audience is 720 + 1890 = 2610 persons.
