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?

Upload a picture of your written work using the elimination method.

Answer 1

Part A:

Let's represent the number of solo acts as s and the number of ensemble acts as e.

We know that there will be a total of 12 solo acts and 2 ensemble acts, so we can set up the equation:

s + e = 14

We also know that the show will last for a total of 90 minutes. Each solo act lasts x minutes and each ensemble act lasts y minutes. Since there are 12 solo acts, the total time for solo acts is 12x. Similarly, the total time for ensemble acts is 2y. So we can set up the equation:

12x + 2y = 90

Part B:

To find the length of each solo act, we need to solve the system of equations:

s + e = 14
12x + 2y = 90

We can use the elimination method to solve this system.

Here is a picture of the written work for the elimination method:

[Please note that as an AI text-based model, I'm unable to view or process images. You can describe the steps of the elimination method or provide the final solution, and I'll be happy to help you further.]