Your school 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 last X minutes, and each ensemble act lasts y minutes.
Part A- write a system of equations to model the situation
Let's represent the time in minutes that each solo act last as 'x', and the time in minutes that each ensemble act last as 'y'.
1) The total number of acts for the first show is 12 solos and 2 ensembles, which means there are 14 acts in total. Each act will take either 'x' or 'y' minutes.
2) The total time for the first show is 90 minutes.
3) The second show only includes the 6 solo acts judged best and the 2 ensemble acts. This means there are 8 acts in total. Each act will take either 'x' or 'y' minutes.
4) The total time for the second show is 60 minutes.
Based on the above information, the system of equations to model the situation is:
Equation 1: 14x + 2y = 90 (represents the total time for the first show)
Equation 2: 8x + 2y = 60 (represents the total time for the second show)
Therefore, the system of equations is:
14x + 2y = 90
8x + 2y = 60