Question

Your​ school's talent show will feature 8 solo acts and 3 ensemble acts. The show will last 93 minutes. The 4 solo performers judged best will give a repeat performance at a second 69 minute​ show, which will also feature the 3 ensemble acts. Each solo act lasts x​ minutes, and each ensemble act lasts y minutes. Use this information to answer parts ​(a) and ​(b).

How long was the solo act?

Answer 1

Each solo act lasted 6 minutes.

Explanation:

Let x be the length of each solo act and y be the length of each ensemble act. We are given that the talent show will feature 8 solo acts and 3 ensemble acts, and the show will last 93 minutes. Therefore, the total time of the solo acts is 8x minutes and the total time of the ensemble acts is 3y minutes. We can represent this information with the following equation:

8x + 3y = 93

We are also given that the best 4 solo performers will give a repeat performance at a second show that will last 69 minutes. Therefore, the total time of the solo acts at the second show is 4x minutes. We can represent this information with the following equation:

4x + 3y = 69

To find the length of each solo act, we can solve the system of equations formed by these two equations. We can do this by first multiplying the first equation by 2 and the second equation by 2, which gives us the following equations:

16x + 6y = 186

8x + 6y = 138

We can then subtract the second equation from the first equation to eliminate y:

8x = 48

Finally, we can divide both sides of the equation by 8 to solve for x:

x = 6