Your school 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 last X minutes, and each ensemble act lasts y minutes.

Question

Your school 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 last 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

Let's assume that each solo act lasts for X minutes and each ensemble act lasts for Y minutes.

Part A:
We are given the following information:
- The total number of solo acts is 12.
- The total number of ensemble acts is 2.
- The total duration of the talent show is 90 minutes.

We can set up the following equations:
Equation 1: 12X + 2Y = 90 (This equation represents the total duration of the talent show)

Equation 2: 6X + 2Y = 60 (This equation represents the duration of the second show, which includes the 6 best solo acts and the 2 ensemble acts)

Part B:
To find the duration of each solo act, we can solve Equation 1 for X:
12X + 2Y = 90
12X = 90 - 2Y
X = (90 - 2Y)/12

So, each solo act lasts for (90 - 2Y)/12 minutes.