Scenario: the talent show
instructions:
view the video found on page 1 of this journal activity.
using the information provided in the video, answer the questions below.
show your work for all calculations
here is a summary of the scenario your classmate presented for the talent show:
main show the main show will last two hours and will include twelve individual acts and six group acts.
final show the final show will last 30 minutes and will include the top four individual acts and the top group act.
the equations he came up with are:
12x + 6y = 120
4x + y = 30
1. what do x and y represent in this situation? (2 points: 1 point for each variable)

2. do you agree that your classmate set up the equations correctly? explain why or why not. (2 points: 1 point for yes/no answer, 1 for explanation)

3. to combine the equations and solve for one of the variables, you need to eliminate the other variable. how can you change one equation so that one variable is eliminated when the two equations are added? explain and write the new equation. (3 points: 2 for your explanation and 1 for the equation)

4. combine the two equations to eliminate one of the variables, and then solve for the other. (3 points: 1 for eliminating one variable, 1 for the answer, and 1 for showing your work)

5. solve for the other variable. (2 points: 1 point for the answer, 1 for showing the work)

6. prove that your solutions are correct by substituting the values back into the original equations and verifying the answers. (2 points)

another way to check your answer is with graphing. the two equations are graphed below.

7. what are the coordinates of the intersection point? does this match your answer from question 4? (2 points: 1 point each question)

8. answer the original questions. (2 points: 1 point each question)
a) how long is each individual act?

b) how long is each group act?

9. discussion.
discuss the reasonableness of your answers. (2 points: 1 point for each part)
a) is the answer you found reasonable? does it seem like enough time?

b) would a negative solution such as (–5, –10) be acceptable in this situation? why or why not?