Your school's talent show will feature 10 solo acts and 3 ensemble acts. The show will last 90 minutes. The 5 solo performers judged best will give a repeat performance at a second 60 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.
A. 3x + 10y = 60 3x + 5y = 90
10x + 3y = 90 5x + 3y = 60 C.
OB. 3x + 10y = 90 3x + 5y = 60
10x + 3y = 60 5x + 3y = 90 D.
b) Solve the system from part (a).
(Type an ordered pair.)
a) The correct system of equations to model the situation is:
3x + 10y = 90
5x + 3y = 60
b) To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of elimination:
Multiplying the first equation by 3 and the second equation by 10, we get:
9x + 30y = 270
50x + 30y = 600
Now, subtracting the second equation from the first equation:
(9x + 30y) - (50x + 30y) = 270 - 600
-41x = -330
Dividing both sides of the equation by -41:
x = 330/41
x ≈ 8.05
Substituting the value of x into the first equation:
3(8.05) + 10y = 90
24.15 + 10y = 90
10y = 90 - 24.15
10y ≈ 65.85
y ≈ 6.59
Therefore, the solution to the system of equations is approximately (8.05, 6.59).