Question

Your school's talent show will feature 8 solo acts and 3 ensemble acts. The show will last 89 minutes. The 4 solo performers judged best will give a repeat performance at a second 61 minute show, which will also feature the 3 ensemble acts. Each solo act lasts x minutes, and each ensemble act lasts y minutes. Write a system of equations to model the situation.

Answer 1

A system of equations to model the time allocation for a school's talent shows can be written as two linear equations: 8x + 3y = 89 for the first show and 4x + 3y = 61 for the second show, where x is the duration of solo acts and y is the duration of ensemble acts.

Step-by-step explanation:

To write a system of equations for this situation, we account for the total time allocated to each school show. The first equation represents the first talent show that lasts 89 minutes with 8 solo acts and 3 ensemble acts. The second equation represents the repeat performance of the second 61-minute show with the 4 top solo performers and 3 ensemble acts.

The system of equations will be:

1. 8x + 3y = 89 (First show with all performers)
2. 4x + 3y = 61 (Second show with top solo performers and ensemble acts)

Here, x represents the duration of each solo act, and y represents the duration of each ensemble act.