Let the number of minutes each solo act lasts be x.
The 14 solo acts will therefore last a total of 14x minutes.
The 3 ensemble acts will last a total of 3y minutes.
The total duration of the talent show is 114 minutes, so we have the equation:
14x + 3y = 114.
In the second show, the 7 solo performers judged best will perform again. The duration of this show is 72 minutes, so we have the equation:
7x + 3y = 72.
We can now solve this system of equations to find the values of x and y.
To do this, we can multiply the second equation by 2 to eliminate y:
14x + 6y = 144.
Subtracting this equation from the first equation will eliminate x:
(14x + 3y) - (14x + 6y) = 114 - 144,
-3y = -30,
y = 10.
Substituting this value of y into the first equation, we can find x:
14x + 3(10) = 114,
14x + 30 = 114,
14x = 84,
x = 6.
Therefore, each solo act lasts 6 minutes and each ensemble act lasts 10 minutes.
(a) Each solo act lasts 6 minutes and each ensemble act lasts 10 minutes.
(b) The duration of the talent show is 114 minutes. The duration of the second show is 72 minutes.
Your school's talent show will feature 14 solo acts and 3 ensemble acts. The show will last 114 minutes. The 7 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. Use this information to answer parts (a) and (b).
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