# The Party Plan

### Math Reprenitation

## Restaurant choice

**Pizza Palace and ****Burger Bonanza are the two we can chose between. **Burger Bonanza **charges $10 pr person and a catering fee of $20. ****Pizza Palace charges $9.25 per person with a setup fee of $61.25.**

**Pizza Palace is cheaper for over 100 students but **Burger Bonanza is cheaper for less than 100 students

The equation to calculate the cost is y=mx+b or y=kx. Pizza Palace rate of change is y=9.25x+61.25 and Burger Bonanza rate of change is y=10x+20

## Question (A)

1. Describe how you created each equation.

First I made out a chart with the information plugged the numbers in. The applied the formula y=kx or y=mx+b to the chart.

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.

First you find a formula for the two separate companies information and change the x from 1 to 2 to 3..... at the same time until the y value are the same or "cross" each other.This situation they both cost the same at 50 people at $520.

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?

At the Burger Bonanza you can only have a maximum of 960 people. At Pizza Palace you can only have maximum of 101 people. You can not, because you can not a fraction of person.

## Proposed plan (A)

**required**.

## Obstacle course

Jumpin’ Jack’s and Hoppin’ Around are our only choices to rent from. Hoppin’ Around charges $75 per hour. Jumpin’ Jack’s charges $54 dollars per hour and $84 fee for set-up an removal.

Hoppin’ Around is cheaper for 4 hours or below but Jumpin’ Jack’s is cheaper for 4 hours or over 4 hours.

The equation to calculate the cost is y=mx+b or y=kx. Jumpin’ Jack’s rate of change y=54x+84 and Hoppin’ Around rate of change is y=75x.

## Question (B)

1. Describe how you created each equation.

First I made out a chart with the information plugged the numbers in. The applied the formula y=kx or y=mx+b to the chart.

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.

First you find a formula for the two separate companies information and change the x from 1 to 2 to 3..... at the same time until the y value are the same or "cross" each other. In this situation they both cost the same at 4 hours wicth cost $300.

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? 10 hours for both companies. Yes because, hours can be broken up into minutes.

## Proposed Plan (B)

**Jumpin’ Jack’s if the hours we are renting are above 4 hours. But if the hours are below 4 hours of renting we go with**

**Hoppin’ Around due to the amount of payment.**