# 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!

## Which Company?

There was 2 food places that I have decided to order from that would be cheap for the party

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

X-Axis = Number of Student's

Y-Axis = Cost (\$)

## Tables

There are 2 graphs shown below. One for Burger Bonanza and Pizza Palace. In the graph you can see the number of students given and how much it will cost for both company's.

## Question 1 - Burger Bonanza/Pizza Palace

Q) - Describe how you created each equation

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

## Question 2 - Burger Bonanza/Pizza Palace

Q) - 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.

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

Now you have the answer for x-55. Now we use that number to calculate the y in the coordinate point. You then have to take the x value and plug it into one of the equations from one of the company's and then solve for y as shown below. The point of intersection is (55,570) on the coordinate graph. This means that if there is 55 students that attend, then both company's would have the same cost which is \$570

## Question 3 - Burger Bonanza/Pizza Palace

Q) 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?

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

I got the same answer for both Burger Bonanza and Pizza Palace for the questions so they are slashed above.

## Proposed Plan

Both company's are cheap but each one has the ups and downs. For Burger Bonanza it is cheaper when there is less number of student's. For Pizza Palace it would be cheaper if there was more student's. Burger Bonanza would be a good choice if you had 55 or less number of student's. But if there is more than that, it would be Pizza Palace.

## Entertainment/Activity for the Party

Now that we have the choice of food, we need the fun. I have decided to get a bounce house or a inflatable obstacle course. These are the most cheapest company's I found to rent from. Hoppin' Around and Jumpin' Jack's Bounce Houses
The equations for each company are shown below

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

Hoppin' Around: y = 75x

Here is a graph I used to compare both companies

## Tables

For the entertainment, shown below are 2 tables. 1 for Hoppin' Around and Jumpin' Jack's. You can understand it easier!

X/left side = number of hours

Y/right side = cost (\$)

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

Q) Describe how you created each equation.

A) I used the poster and table to calculate it

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

Q) 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.

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

Now that we have the x for the coordinate point of intersection, we need to find the y. First we have to choose an equation either from Hoppin' Around or Jumpin' Jack's. I chose the one from Jumpin' Jacks. So, then you have to plug in the x in that equation with 4 and solve it. The answer is 300 for the y. The final answer in coordinate form is (4,300). In word form that means both company's charge the same amount of money (\$300) fo 4 hours.

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

Q) 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

I chose the cheapest company's, for both entertainment and food.

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!