Part A:
Let's denote the duration of each solo act as x and the duration of each ensemble act as y. The total number of acts in the talent show is 12 solo acts and 2 ensemble acts, so the total number of acts is 12 + 2 = 14.
The first show lasts 90 minutes, and the second show lasts 60 minutes. The 6 solo performers judged best will give a repeat performance at the second show. So, the duration of the first show can be represented as:
12x + 2y = 90 (Equation 1)
And the duration of the second show can be represented as:
6x + 2y = 60 (Equation 2)
Part B:
To find the duration of each solo act, we need to solve the system of equations.
Let's solve Equation 1 for y:
2y = 90 - 12x
Divide both sides by 2:
y = 45 - 6x/2
y = 45 - 3x
Now substitute this value of y in Equation 2:
6x + 2(45 - 3x) = 60
6x + 90 - 6x = 60
90 = 60
This equation is not possible to solve for x as it results in an inconsistency. Therefore, we cannot determine the duration of each solo act with the given information.
Your school's 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 lasts x minutes, and each ensemble act lasts y minutes.
Part A
Write a system of equations to model the situation.
Part B
How long is each solo act?
1 answer