Your school's talent show will feature 12 singing acts and 2 dance acts. The show will last 98 minutes. The 6 singing acts judged best will give a repeat performance at a second 62 minute show, which will also feature the 2 dance acts. Each singing act lasts x minutes, and each dance act lasts y minutes.
write some systems of equations that model this situation.
Let's start by defining the given information:
Number of singing acts = 12
Number of dance acts = 2
Total duration of the talent show = 98 minutes
Duration of the second show = 62 minutes
Now, let's define the variables:
Let x be the duration of each singing act in minutes.
Let y be the duration of each dance act in minutes.
Let n be the number of singing acts that give a repeat performance in the second show.
Based on this information, we can write the following system of equations to model the situation:
Equation 1: 12x + 2y = 98
This equation represents the total duration of the first show, which is 98 minutes, and includes 12 singing acts (each lasting x minutes) and 2 dance acts (each lasting y minutes).
Equation 2: (6+n)x + 2y = 62
This equation represents the total duration of the second show, which is 62 minutes, and includes n singing acts that give a repeat performance (each lasting x minutes) and 2 dance acts (each lasting y minutes).
Note: The value n represents the number of singing acts that give a repeat performance in the second show. We don't have enough information to determine the exact value of n, but it should be between 0 and 6 (inclusive) since only 6 singing acts will be selected to perform again.