Your school's talent show will feature 16 solo acts and 3 ensemble acts. The show will last 126 minutes the 8 solo performers judged best will give a repeat performance at a second 78 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).
a) Write a system of equations to model the situation.
16x+3y=126
8x+3y=78
b) Solve the system from part (a).
(Type an ordered pair.)
To solve the system of equations, we can use the method of substitution or elimination.
Using the method of elimination:
We subtract the second equation from the first equation to eliminate the y term:
(16x + 3y) - (8x + 3y) = 126 - 78
8x = 48
x = 6
Now, we substitute the value of x into either equation to solve for y:
16(6) + 3y = 126
96 + 3y = 126
3y = 126 - 96
3y = 30
y = 10
Therefore, the solution to the system of equations is (x, y) = (6, 10).
How long is each solo act?
minutes