Part A
Let's represent the number of solo acts with S and the number of ensemble acts with E.
The total number of acts in the first show is 12 solo acts plus 2 ensemble acts, so S + E = 14.
The total duration of the first show is 90 minutes, and each solo act lasts x minutes, and each ensemble act lasts y minutes. Therefore, the total duration can be represented as:
12x + 2y = 90.
Part B
To find the duration of each solo act, divide the total duration of the first show by the number of solo acts:
x = (90 - 2y) / 12.
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?
1 answer