# 7th Grade Party

### By: Aysia Lewis

## Grab Some Grub

**Burger Bonanza Equation:**y=10x+20

**Pizza Palace Equation: **y=9.25x+61.25

**Point of Intersection: **At 55 people, it will cost $570 for both companies

## Purposed Plan

If more than 55 people go to the party, Pizza Palace would be the better deal. If less than 55 people go to the party, Burger Bonanza would be the better buy

## Describe how you created each equation.

I created my equations by looking at each flyer for the company. The flyer for Burger Bonanza said $10/person. I knew the x would be the amount of people and the $10 would be the rate of change. It also said a $20 catering fee. I knew that would be the y intercept.

Based on the information, I got the equation of y=10x+20. For Pizza Palace, I knew it cost $9.25 per person so the $9.25 would be the rate of change. I also knew the x would be the amount of people. The flyer said there was a $61.25 set up fee so I knew that was the y intercept. From this information, I got the equation of y=9.25x+61.25.

## Will there be a number of students where both companies will cost the same?

Yes, there will be a number of students where both companies will cost the same. At 55 students, it will cost $570 for both companies. I got this answer by putting an equal sign between each equation. I then solved for x. I did this by cancelling out one of the x values. Next I cancelled out the 20 and subtracted 20 from 61.25. Finally, I divided .75x and 41.25 by .75 to get 55.

## 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?

If I only had a $1,000 budget, 98 people, maximum would be able to come for Burger Bonanza. However, 101 people, maximum would be able to come for Pizza Palace. You can not have a fraction or decimal as part of you answer because you can not have part of a person go to the party.

## Bounce House

**Jumvinbpin' Jack's Equation:**y=54x+84

**Hoppin' Around Equation: **y=75x

**Point of Intersection: **At 4 hours, both companies will cost $300.

## Proposed Plan

If the party lasts 0-4 hours, Hoppin' Around would be better. It would be cheaper to use that company. If the party lasts more than 4 hours, Jumpin' Jack's would be better.

## Describe how you created each equation.

I looked at the flyers to create each equation. For Hoppin' Around, it said it cost $75/hour. I knew the $75 would be the rate of change. I also knew the x would be the amount of hours. From this information, I got the equation y=75x. For Jumpin' Jack's I knew it cost $54 per hour. I knew that would be the rate of change and the number of hours would be the x. I also noticed there was an $84 set up/removal fee. I knew the set up and removal fee would be the y intercept. Based on this information, I got y=54x+84 as the equation.

## Will there ever be a number of students where both companies will cost the same?

Yes, there will be a number of students where both companies will cost the same. At 4 hours, it will cost $300 for both companies. I used the same steps as the previous one to figure this out.

## 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?

If I only have a $750 budget, about 12.33 hours, maximum, for Jumpin' Jack's. If I were using Hoppin' Around, I would be able to have 10 hours of the bounce house. You can have a decimal/fraction as part of my answer because you can have part of an hour.