Question

Your​ school's talent show will feature 12 solo acts and 3 ensemble acts. The show will last 102 minutes. The 6 solo performers judged best will give a repeat performance at a second 72 minute​ show, which will also feature the 3 ensemble acts. Each solo act lasts x​ minutes, and each ensemble act lasts y minutes

Answer 1

each solo act will last 5 minutes and each ensemble act will last 14 minutes

Explanation:

In the first show, we are told that there are 12 solo acts and 3 ensemble acts.

Now since each solo act lasts x​ minutes, and each ensemble act lasts y minutes and the show lasts 102 minutes, thus we have;

12x + 3y = 102 - - - - eq1

In the second show which lasts 72 minutes, we are told that there will be 6 solo acts and 3 ensemble acts.

Thus,we have;

6x + 3y = 72 - - - - eq2

Now, let's find x and y by subtracting eq 2 from eq1 to give;

6x = 30

Divide both sides by 6 to give;

x = 5

Put 5 for x in eq2;

6(5) + 3y = 72

30 + 3y = 72

3y = 72 - 30

3y = 42

y = 42/3

y = 14

Thus, each solo act will last 5 minutes and each ensemble act will last 14 minutes