High School Mathematics Problems from Alaska

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Standards: Functions and Relationships. 

Performance Standards: A4.4.2, A4.3.4, A4.3.5

Concepts: Representing relationships between variables by writing, creating, and solving linear equations, and using tables and graphing.

Carnegie Chapter: Proportional Reasoning and Percentages.

Overview: Focusing on writing and using the results of a linear equation and graphing a linear equation.

Fundraiser - Ticket Sales

Problem 7

The Junior Class has decided to show movies in order to raise money for the prom. They found that the rights to show a movie for a weekend cost $325 and feel that $5 is a fair admission price.

Please answer all questions in the form of complete sentences.

1. How much profit will be made if they have:
   1. 100 paying customers?
      
      
      
   2. 264 paying customers?
      
      
      
   3. 512 paying customers?
      
      
      
   4. 40 paying customers?
      
      
      
   5. What methods did you use to calculate the profit?
      
      
      
   6. What does your answer from part D mean?

2. How many customers are needed for the class to "break even?"

1. How did you calculate this?
   
   
   
   
   
   
   
2. Write an equation for profit based upon the number of people who came to the show.

3. Using the formula that you just wrote, how much profit will be made if they have:
   1. 214 paying customers?
      
      
      
      
   2. 673 paying customers?
      
      
      
      
   3. 169 paying customers?

4. The Junior Class needs to make $900 in order to finish paying for the prom. How many customers will they need in order to make their goal?

1. What if they need $2000?
   
   
   
   
2. What if they need $3000?
   
   
   
   
3. What if they need $5000?

5. One year, a group decided to show the movie, Seven Years in Tibet, and they had a very poor turnout. (In fact, the turnout was so poor that the group decided to cancel the final screening.) Assuming that they paid the standard rate for the movie, and had three screenings with twelve, three, and five customers:
   1. What was the final outcome for the group? Be sure to justify your answer.
      
      
      
      
      
   2. Besides the financial situation, why else might the group be frustrated with this outcome?

6. Complete the following table that uses information from the above problems:

7. Using the information from the table above graph it on the axes below. Be sure to include all labels.

8. Using the graph, estimate:
   1. How many customers they will need in order to get a profit of $1000.
      
      
      
      
      
   2. How many customers they will need in order to get a profit of $4000.
      
      
      
      
   3. The profit generated by 250 paying customers.

9. Assume that the theater can hold 200 people. What is the minimum number of screenings that you will need in order to make your goal for each part of problem 5?

a)

 

b)

 

c)

d)

10. A group of six people sneaks into the movie through the back door, taking the last available seats. How much money will the class lose? (Be sure to justify your answer.)

For the Teacher's Guides, please email Alaska Native Knowledge Network

Handbook for Culturally Responsive Science Curriculum by Sidney Stephens
Excerpt: "The information and insights contained in this document will be of interest to anyone involved in bringing local knowledge to bear in school curriculum. Drawing upon the efforts of many people over a period of several years, Sidney Stephens has managed to distill and synthesize the critical ingredients for making the teaching of science relevant and meaningful in culturally adaptable ways."