# 7th grade End of Year Party

### By: Hailey Williams

## What is the problem?

I have decided that the 7th grade deserves a huge party at the end of the year to reward them for all of their hard work. However, rather than make all the decisions myself, I felt that it would be better for 7th graders to make the decisions on what types of things would make a great party. I have compiled a list of different activities that have worked well in the past, and have found some pricing for various companies that offer these activities.

Unfortunately, I haven’t gotten around to comparing any of these prices yet or calculating which one would be best. I’m not sure how long this party will last, so I would like to have a range of times to choose from. I am also not sure how many of our 7th grade students will be participating in this party, so I need pricing for various numbers of students. As I know you have studied patterns, equations and rates of change so far this year, I know you will be able to help plan a spectacular party. Let’s go over what your party should have:

Ø Food

Ø Bounce House

Those are the “must haves” for your party. If you feel like you should add anything else, feel free to do so. In addition to the above, you still have to convince me that your ideas are the best way to go for this party. So once you have finished making your informed decisions, you’re going to have to “WOW” me with your ideas. Try putting your ideas into some kind of eye catching presentation, like a Smore, a Prezi, or a website like Weebly. I have given this task to all the 7th graders, so your job is to convince me that you are the best candidate for the job. Good luck and have fun planning!!!

Sincerely,

Chris Jones

Principal of Gene Pike Middle School

## Grab Some Grub!

## More information:

**Part A – Grab Some Grub**

Note -

Two companies have worked with us in the past to provide food for students whenever we have a party day. Recently, however, the companies have come under new management. This means that their prices may have changed a bit since the last time we used them. I managed to get some flyers from them regarding their rates for large orders of food, but I haven’t had a chance to check them out. Take a look at these flyers, and see what you make of them.

- C. Jones

## How did you get these answers?

## Critical Thinking Questions

## 1. Describe how you created each equation.

I created this equation by looking at the information that was given on the flyer and I filled it into the equation y=mx+b. Y is the total amount in this representation and the m is the price per person that orders. X represents the # of people because it is an independent variable. Finally, I thought that b should represent the catering fee because you are adding it to the price of the total price of the people.

## 2. Will there ever be a number of students where both companies will cost the same? Describe the steps you would use and then solve for the number of students for which both companies will cost the same amount.

There will be a # of horses that the companies will be the same. Both of the food places will cost the same after 55 hours. I know this because I set the equations equal to each other. I subtracted one x from the other then, I did my whole amounts. Finally, I divided the x value by the whole value that was left. (Look at the photo)

## 3. If you only have a budget of $1000 for food, how many people, maximum, would you be able to have at the 7th Grade Blowout for each company? Can you have a decimal or fraction as part of your answer? Why or why not?

98 people maximum can attend and order at Burger Bonanza if they had a budget (with no tax) of $1000 for food. 101 people maximum can attend and order at Pizza Palace if they had a budget of $10000. You should not have a decimal of fraction as part of your answer because there is no “parts” of a person.

## My proposed plan

**My plan is to have a very fun party with the cheapest price that you have to pay. If you are keeping catering the food for less than an hour (prep time) then Burger Bonanza would be the best choice. They only charge you $20 for 0 hours. This is a $41.25 difference for possibly, driving out of the driveway (If you pick Pizza Palace)! The statistics are the same for an hour up to 50 hours, the price for Burger Bonanza is 1020. However, the price for Pizza Palace for 100 hours is 986.25. For 150 hours at Burger Bonanza is 1520. After using the food for 150 hours at Pizza Palace, you have to pay a total of $1448.75. I don’t think you are having longer than a 50-hour party so Burger Bonanza is the best deal. However, if you have to keep it for longer than 50 hours, than Pizza Palace is the better deal. The price of Burger Bonanza goes up increasingly quickly when, on the other hand, Pizza Palace goes up quickly but, in small increments. **

## Bounce House

## How did you get these answers?

## Critical Thinking Questions

## 1. Describe how you created each equation

I created this equation by looking at the flyer and filling in the amounts. For instance, when I saw that it was $75 per hour, I knew that the “per hour” would represent the X value. The M value would definitely represent the $75 dollars because it is the unit rate. In this instance, there is no b. I know this because it says nothing about a catering fee or a ordering fee that you would add the amount of money that needs to be paid per hour. The Y value would definitely be the Total cost because it is the dependent variable.

## 2. Will there ever be a number of hours where both companies will cost the same? Describe the steps you would use and then solve for the number of hours for which both companies will cost the same amount.

The price per person will be the same after 4 hours. The cost will be $300. I found this answer by #1: Looking at the table. The amounts are the same on there. However, if it does not tell you when they will be equal, then you can set the equations equal to each other. However, the easier way is to compare the graphs.

## 3. If you only have a budget of $750 for the bounce house, how many hours, maximum, would you be able to have at the 7th Grade Blowout for each company? Can you have a decimal or fraction as part of your answer? Why or why not?

If you only have a budget of $750 for bounce a house, you would be able to keep a jumpin jacks bounce house for 12.3 hours. If you only had a budget of $750 for a bounce house, you would be able to keep a Hoppin’ around bounce house for 10 hours.

It would make sense to have decimals in this instance because there are parts of an hour. But, the decimals must stop, no rounding at the tenths place.## My Proposed plan

**My plan is to use Hoppin’ around from 0-3 hours and Jumpin for 5 hours and up. This is because for Jumpin’, there is an upfront fee but, after 5 hours, the total cost is $354 on the other hand, the total price for 5 hours it costs $375. The pattern keeps going. For example, for 6 hours, the total price for Jumpin’ Jack is $408. For Hoppin’, for 6 hours, the total price is $450. Finally, after 10 hours, the cost for Jumpin’ is $624. The price for Hoppin’ is $750. If you need to rent the bounce houses for 4 hours, you can pick whichever company you please. After that, from 5- any greater # hours, Jumpin is the better deal. Therefore, if you are holding the party for more than 4 hours, your best choice is Jumpin’.**