# Planning a party

## 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

We were asked to figure out the prices for two different companies. Pizza palace and burger bonanza. Burger bonanza cost \$10 per person with a one time catering fee of \$20, giving each student their choice of 1 vegetarian, beef, or chicken burger. Pizza palace charges a fee of \$61.25 and cost \$9.25 per person, that gets an all you can eat buffet.

## key for graph

red> Burger bonanza

Green>pizza palace

## Budget limited to \$1000 for food.

We ended up having to spend less or equal to \$1000. so i figured out how many students we could have for each

>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

I propose we use pizza palace not only for the fact we could afford more students to come to the party, but the students are able to get as much pizza as they want. Also b/c it is cheaper to cater with pizza palace for any more than 55 kids.

## Step 2: bouncy house

we were also asked to have an attraction something fun to do so we chose to have some kind of blow up attraction.We were presented with 2 companies Hoppin around, and Jumpin jack's bounce houses. Hoppin around cost \$75 per hour per bounce house. jumpin jacks cost \$54 per hour and a set up and removal fee of \$84.

## key for chart

red> jumpin' jacks

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.

Yes the lines cross at the coordinates (4,300). i found this out by writing each equations left side = to the other then i solved for x. This gives me my x-value, which i then plug into either of the equations to get my y-value.

## 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?

We had a budget of \$750 for the bouncy house we wanted to have a nice bounce house for a good amount of time say like 5 hours but with us spending only \$750 we could afford this many hours:

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.

## Bouncy house: proposal

I propose we rent a bouncy house from jumpin' jacks for 5 hours b/c we don't need it any longer than that and its cheaper to rent from jumpin' jacks for 5 hours than from hoppin' around