Task : “Decorating for the Dance” Name ______

The 7th Grade class is responsible for planning the Winter Dance. Sarah is the chairperson of the decorating committee and knows that if she had to decorate the gym alone it will take her 40 hours. Sarah said, “The more people that help, the quicker we will get the job done.” Help her estimate how much time it will take to decorate the gym.

1. Describe the relationship between the number of people working and the amount of time it will take to decorate the gym. ______

______

2. How much time would it take for 2 people to decorate the gym? Four people? Complete the table including 1-8 people working and decorating times for each number.

Number of People Working / Hours to Decorate the gym
1 / 40
2
3
4
5
6
7
8

How did you determine the amount of time each group would work? ______

______

3. Create a graph to represent the situation.

Hours to Decorate
30
10
1 / 3 / 5 / 7 / 9
Number of People

What do you notice? ______

4. Could the point (2.5, 16) be on this graph? Explain why or why not. (remember the x coordinate in this case shows the number of people working) ______

5. Would this graph ever cross either of the axes? Explain why or why not. (could you ever decorate in 0 hours? Could you ever decorate with 0 people?)______

______

6. Is this graph directly or inversely proportional? Justify your answer. ______

______

______

7. Write an equation that shows the relationship between the time it will take to decorate the gym and the number of people working. ______

8. How is the factor of change in the number of students working related to the factor of change in the total number of hours to decorate? ______

______

9. What is the constant of proportionality and what does it represent? ______

The ticket committee has decided to charge $3.50 for each ticket to the St. Patrick’s Day Dance.

10. Describe the relationship between the number of tickets sold and the amount of money collected.

______

11. How much money would be collected if 25 students bought tickets? 50 students? Complete the table.

# of Tickets / 25 / 50 / 75 / 100 / 125
Total Income

12. Create a graph to represent this situation. What do you notice?

Total Sales in Dollars / 500
300
100
25 / 75
# of Tickets sold

13. Could the point (-4, -14) be on this graph? Explain why or why not. ______

______

14. Would this graph ever cross either of the axes? Explain why or why not. (could you sell 0 tickets or take in 0 dollars?) ______

15. Is this graph directly or inversely proportional? Justify your answer. ______

______

16. Write an equation that shows the relationship between the number of tickets sold and the total amount of money collected. ______

17. What is the constant of proportionality and what does it represent? ______

18. If the 7th grade class spent $225 on the dance, how many tickets do they need to sell to cover their costs? Justify your answer. ______

______