# Planning a Party Project

## Background Information/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:

• Food

• Bounce House

## Critical Thinking Questions Part A

1. Describe how you created each equation.

I know I needed to set up my equation in the form Y=kx, so first I found my dependent and independent variables. I could tell from the flyer that it said food from burger bonanza was 10 dollars per person plus a 20 dollar catering fee, this shows the total cost would depend on the number of people that need food. This means that the total cost is y and the number of people would be x. I also noticed the 20 dollar catering fee this showed that the equation would have to be written in the form Y=mx+b because the Y-intercept is not 0 it is 20. So I got the equation Y=10x+20 x being the number of people and y being the total cost. I did a very similar thing foor pizza palace because it too also has a y intercept the difference was it was 9.25 per person and a 61.25 catering fee. So my equation was Y=9.25x+61.25

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.

Yes they will be the same. I started by plugging 350 in for X. Then I subtracted the answered from the equations and realized they had a big difference. So then I realized instead of going up with the number of people I needed to go down with the number of people. I tried multiple different numbers until I got to 55 and found out that both the pizza palace and burger bonanza had 570 as the cost.

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?

For burger bonanza the maximum number of people you could have for a budget of 1000 dollars is 98. For pizza palace the maximum number you could have is 101. You cannot have a fraction or decimal for this question because it is not possible to have a fraction or part of a person.

## Proposed Plan Part A

At 55 students the price is the same, so you could choose either company. If you are buying food for 54 students or less, burger bonanza is the best deal. If you are buying food for 56 students or more, pizza palace is the better deal.

## Critical Thinking Questions Part B

1. Describe how you created each equation.

I know I needed to set up my equation in the form Y=kx, so first I found my dependent and independent variables. I could tell from the flyer that it said for hopin’ around it was 75 dollars per hour. This shows the total cost would depend on the number of hours you rent the bounce house. This means that the total cost is y and the number of hours would be x. So I got the equation Y=75x, x being the number of hours and y being the total cost. I did a similar thing for jumpin’ jacks because it too was Y for the total cost and X for the number of hours. It was 54 dollars per hour. The difference was this one had an 84 dollar set up fee, the 84 being the Y=intercept s I used the form Y=mx+b. This made the equation Y= 54x+84

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.

Yes, at 4 hours they will both cost 300 dollars. You don’t have to solve for it because it is in the table but if you were to you would plug innumbers into the equations until they both equaled the same number.

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?

For hopin’ around you would be able to have 10 hours max with a budget of 750 dollars. For jumpin’ jacks you would be able to 12.33 repeated or 12 1/3 hours with a budget of 750 dollars. You can use fractional parts because you can have parts of an hour.

## Proposed Plan Part B

At 4 hours both companies are a good deal because they will both cost 300 dollars. If you are renting the bounce house for 4 dollars or less hopin’ around is a better deal. If you are renting the bounce house for 5 hours or more jumpin’ jacks is a better deal.