Your school's talent show will feature 12 solo acts and 3 ensemble acts. The show will last 111 minutes. The 6 solo performers judged best will give a repeat performance at a second 75 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).

Question

Your school's talent show will feature 12 solo acts and 3 ensemble acts. The show will last 111 minutes. The 6 solo performers judged best will give a repeat performance at a second 75 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).

Write a system of equations to model the situation.
A.
12 x plus 3 y
equals
111
6 x plus 3 y
equals
75

B.
3 x plus 12 y
equals
75
3 x plus 6 y
equals
111

C.
12 x plus 3 y
equals
75
6 x plus 3 y
equals
111

D.
3 x plus 12 y
equals
111
3 x plus 6 y
equals
75

olve the system from part (a).
nothing (Type an ordered pair.)
How long is each solo act?
nothing minute(s)
How long is each ensemble act?
nothing minute(s)

Answer 1

i chose a for part a, but i need help with the ordered pair then

Answer 2

A is correct, but do you have a problem with + and - and = signs?

12x+3y = 111
6x+3y = 75
clearly the only difference here is the extra 6 solos, so subtract to get
6x = 36
x = 6
Now you can find y

Answer 3

The correct answer is A. 12x + 3y = 111 and 6x + 3y = 75.

To solve the system of equations, we can use either substitution or elimination method. Let's use the elimination method:

Multiply the second equation by 2: 2*(6x + 3y) = 2*75
This gives us: 12x + 6y = 150

Now, subtract the first equation from the second equation:
(12x + 6y) - (12x + 3y) = 150 - 111
This simplifies to: 3y = 39

Solving for y, we get: y = 13

Substitute the value of y back into one of the original equations:
6x + 3y = 75
6x + 3(13) = 75
6x + 39 = 75
6x = 75 - 39
6x = 36

Solving for x, we get: x = 6

Therefore, each solo act is 6 minutes long and each ensemble act is 13 minutes long.

Answer 4

The correct system of equations to model the situation is:

12x + 3y = 111 (equation 1)
6x + 3y = 75 (equation 2)

To solve this system of equations, we can use the method of substitution or elimination.

Let's use elimination method to solve the system.

Multiplying equation 2 by 2, we get:

12x + 6y = 150 (equation 3)

Now, subtracting equation 1 from equation 3, we eliminate the y variable:

(12x + 6y) - (12x + 3y) = 150 - 111
3y = 39

Dividing both sides of the equation by 3, we find:

y = 13

Now, substitute the value of y back into equation 1:

12x + 3(13) = 111
12x + 39 = 111

Subtracting 39 from both sides, we have:

12x = 72

Dividing both sides by 12, we find:

x = 6

Therefore, each solo act lasts 6 minutes and each ensemble act lasts 13 minutes.

Answer:

Each solo act lasts 6 minutes.
Each ensemble act lasts 13 minutes.