Part A: Let's denote the length of each solo act as x minutes and the length of each ensemble act as y minutes.
From the given information, we know that there will be 12 solo acts and 2 ensemble acts in the first show, which lasts 90 minutes. This can be represented by the equation:
12x + 2y = 90
In the second show, the 6 solo performers judged best will give a repeat performance, along with the 2 ensemble acts. The second show lasts 60 minutes, so the total length of the solo acts plus the ensemble acts should be equal to 60 minutes:
6x + 2y = 60
Therefore, the system of equations to model the situation is:
12x + 2y = 90
6x + 2y = 60
Part B: To find the length of each solo act, we can solve the system of equations. Subtracting the second equation from the first equation eliminates the y term:
(12x + 2y) - (6x + 2y) = 90 - 60
6x = 30
x = 5
Therefore, each solo act lasts 5 minutes.
Your school's talent show will feature 12 solo acts and 2 ensemble acts. The show will last 90 minutes. The 6 solo performers judged best will give a repeat performance at a second 60-minute show, which will also feature the 2 ensemble acts. Each solo act lasts x minutes, and each ensemble act lasts y minutes.
Part A Write a system of equations to model the situation.
Part B How long is each solo act?
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