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.

Question

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?

Answer 1

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.