Question

Your schools talent show will feature 12 solo acts and ensemble 2 acts. The show will last 90 min. The 6 solo performers judged best will give a repeat performance at a second 60-min show, which will also feature the 2 ensemble acts. Each solo lasts x minutes, and each ensemble act lasts y minutes.
A. Write a system of equations to model the situation.
B. Solve the system from part(a). How long is each solo act? How long is each ensemble act?

Answer 1

A.  12*x + 2*y = 90
       6*x + 2*y = 60

To write system of equation you just need to sum all solo and ensemble acts and make it equal to how much they will last for.

B.  Here we can multiply second equation with negative 1 and add it to first equation.
6x = 30
x = 5

now we replace x in any of 2 equations to get y.
30+2y = 60
2y = 30
y=15

Solo acts are 5 minutes long and ensemble acts are 15 minutes long