# Planning a party

### Unit 10 project

## The Letter

Dear Riley Russell,

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:

> Food

> 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,

Kim Barker

Principal of Tidwell Middle School

## Step 1: Food

## Tables

## Burger bonanza | ## Pizza palace | ## How i determined the equationsI created the equation for burger bonanza by determining the roc (10) and then figuring out the y-intercept which was 20, so I knew it would be Y= 10x + 20. I found pizza palace’s equation by finding the roc (9.25) and then figuring out my y- intercept which was 61.25. The equation turned out to be Y= 9.25x +61.25. |

## How i determined the equations

I created the equation for burger bonanza by determining the roc (10) and then figuring out the y-intercept which was 20, so I knew it would be Y= 10x + 20. I found pizza palace’s equation by finding the roc (9.25) and then figuring out my y- intercept which was 61.25. The equation turned out to be Y= 9.25x +61.25.

## key for graph

Green>pizza palace

## Budget limited to $1000 for food.

>Burger Bonanza>98

>pizza palace>101

(note: i cant have a decimal form as an amount of people b/c you cant have half of sally come to the party and half stay in class)

## 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.

The students and cost intercept at the points (55,570). I determined this by writing each equation with y on the left side, then set the right sides of each equation = to each other and solved for x to determine the x-value. To find the y value I used the x-value to solve to get y.

## Food: Proposed plan

## Step 2: bouncy house

## Jumpin' jacks | ## Hoppin' around | ## How i found the equations I found the equation for jumpin' jacks by taking the ROC (54) and adding the y intercept which was 84 to = Y. For hoppin' around i noticed that there was no sort of fee or anything similar to a y-intercept so i knew it would be the ROC multiplied by x = Y |

## key for chart

Green>Hoppin' around

## 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.

## 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?

Jumpin' jacks>12.3 hours (repeating)

Hopin' around>10 hours

We can have a decimal for an answer here b/c we can keep a bouncy house for half an hour.