# Planning a Party Project

### By: Abhi M.

**I am planning a party for the 7th grade at the end of the year. I have decided on what company to go to for food and fun. The math shown below are the possible amounts of money to spend and the better company and why. Let's check it out!**

## Food for the Party

## Which Company?

Burger Bonanza: y = 10x + 20

Pizza Palace: y = 9.25x + 61.25

Here is a graph that I used to compare the prices.

## X and Y Axis

Y-Axis = Cost ($)

## Tables

## Critical Thinking Questions

## Question 1 - Burger Bonanza/Pizza Palace

A) - I used the information on the graph to create the equation and the information on the flyers.

## Question 2 - Burger Bonanza/Pizza Palace

A) - Yes, this is called the point of intersection. First you set up the 2 equations together for both company's. Then you have to get the x on one side so you subtract 9.25x on both sides and then that equals .75x and all the other numbers stay the same. Then you have to subtract 20 on both sides to delete it. That then equals 41.25. After that you divide the .75 on both sides and then you get the x in the coordinate point. The work is below.

## Question 2 Continued

## Question 3 - Burger Bonanza/Pizza Palace

A)

Burger Bonanza - 98 students

Pizza Palace - 101 students

A decimal and fraction cannot be a part of an answer because you may be able to have sections in money but not in students. You cannot split a student in half for an answer. So the answer is no.

## Question 1, 2 & 3

## Proposed Plan

## Entertainment/Activity for the Party

Jumpin ' Jack's: y = 54x + 84

Hoppin' Around: y = 75x

Here is a graph I used to compare both companies

## Tables

X/left side = number of hours

Y/right side = cost ($)

## Critical Thinking Questions

## Question 1 - Hoppin' Around/Jumpin' Jack's

A) I used the poster and table to calculate it

## Question 2 - Hoppin' Around/Jumpin' Jack's

A) Yes, it is called the point of intersection. First to find it you have to equal the equations together. Than you have to solve for y. Now you have get the x's on one side. So then you have to subtract 54x on both side to equal it to make: 21x = 84. Finally you have to divide 21 on both sides and the x is by itself. 84/21 is 4. 4 is the x for the coordinate point of intersection.

## Question 2 Continued

## Question 3 - Hoppin' Around/Jumpin' Jack's

**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?**

A)

Hoppin' Around: 10 hours

Jumpin' Jack's: 12 hours

Yes you can have a decimal or a fraction for an answer. This is possible because the x-axis is hours and the y-axis in money. For example, you can 4.6384 of an hour and in money but you cant have it in student's or food and stuff like that. The money and the hours can be divided multiple timesand it would still be reasonable.

Work:

## Final Proposed Plan

Food:

Both company's are good until one point. I think that Pizza Palace would be more necessary because it is cheaper with more people. Burger Bonanza is good until there is 55 student's. Beyond that it would be Pizza Palace. Like it there were 150 people it would cost $1448.75 for Pizza Palace but for Burger Bonanza it costs $1520. Pizza Palace would be more reasonable because there is probably more than about 200 student's in 7th grade. Let alone that most of them will be coming.

Entertainment:

For the bouncy house, the company's I chose are probably the cheapest I could find. Hoppin' Around is cheaper when there is less hours, while Jumpin' Jack's would be better for more hours.They both cost the same ($300) if you rent for 4 hours. Beyond that like 4 and a half it would be cheaper for Jumpin' Jack's because it would cost around $325 and Hoppin' Around would cost around $345. Overall I think it we would rent it for at least 4 hours and it would cost $300. If the student's spend more time or less we can figure that out later, maybe ask the 7th graders for their option on how many hours.

Therefore, I think this party will be a success and the 7th graders will love it. Hope it goes well!