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Dimitri is helping to plan the school talent show. Each performer for the talent show has 6 minutes for his or her performance, which includes transition time between performances. If the introduction for the talent show is 24 minutes long and the entire show, including the introduction, will last 150 minutes, how many different performances can the talent show accommodate?

Dimitri is helping to plan the school talent show. Each performer for the talent show has $6$ minutes for his or her performance, which includes transition time between performances. If the introduction for the talent show is $24$ minutes long and the entire show, including the introduction, will last $150$ minutes, how many different performances can the talent show accommodate?

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Counting principle

Full solution

Q. Dimitri is helping to plan the school talent show. Each performer for the talent show has

6

minutes for his or her performance, which includes transition time between performances. If the introduction for the talent show is

24

minutes long and the entire show, including the introduction, will last

150

minutes, how many different performances can the talent show accommodate?

Determine Time Available: Determine the total time available for performances. The total duration of the talent show is $150$ minutes, and the introduction takes up $24$ minutes. To find the time available for performances, we subtract the introduction time from the total time. Calculation: $150$ minutes (total time) $-$ $24$ minutes (introduction time) $=$ $126$ minutes (time available for performances).
Calculate Number of Performances: Calculate the number of performances that can fit into the available time. $\newline$ Each performance, including transition time, takes $6$ minutes. To find out how many performances can fit into the available time, we divide the time available for performances by the time each performance takes. $\newline$ Calculation: $126$ minutes (time available for performances) / $6$ minutes (time per performance) = $21$ performances.

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