# Planning a Party!

### By: Megan Burnett

## Introduction:

## Food-Burger Bonanza:

Burger Bonanza Offers-

- Chicken, beef, turkey, and vegetarian burger
- Any choice of drink
- Regular, sweet potato fries, chips, or potato soup
- Pickle
- $10 a person
- $20 Catering Fee

## Burger Bonanza: Equation, Table, and Graph

## Food-Pizza Palace:

Pizza Palace Offers-

- 5 Different Variety of Pizza
- 3 Different Variety of Pasta
- Breadsticks
- Salad
- Drink
- $9.25 a person
- $61.25 set up fee

## Pizza Palace: Equation, Table, and Graph

## Critical Thinking Questions: Describe how you created each equation.

**Burger Bonanza**: Well, to make a table you need an equation to help you figure out the total cost for the amount of people you want. So first every equation has the total cost (y=) Then you need to figure out the rate of change. So that would be $10 per person (y=10x) the x represents the amount of people. Then there is a fee for $20 and that would be the y-intercept. So the equation would be- y=10x+20.**Pizza Palace-**We need to take the same steps as before. You always start with the total cost (y=) Then we find the rate of change or cost per person. Which would be (y=9.25x). Next we find the y-intercept which is the fee of $61.25. So our final equation is- y=9.25x+61.25

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

Yes there will become a point where the companies will cost the same. I used an online graph which had a visual of the two lines and there point of intersection. Also if you plug in you x value in each equation you will come out with the same total cost.

**Burger Bonanza**- y=10(55)+20 or (55*10)=550+20=$570**Pizza Palace**- y=9.25(55)+61.25 or (9.25*55) 508.75+61.25=$570

So if you have 55 students then both companies will have the same cost.

## If you have a budget of $1000 for food how many students maxium would you be able to have?

**Burgers Bonanza**- You need the equation for this one. Since we know how much money we can spend, we can remove the y with 1000(1000=10x+20) To figure this out we need to plug in the x to make the total value be $1000 or less than 1000. Lets use the number 98. So 1000=10(98)+20. That would be 98*10=980+20=$1000. Only 98 students, exactly, can attend the party if you pay $1000.

**Pizza Palace**- Again you need to use the equation to help us figure this problem. 1000=9.25x+61.25. Lets use the number 101. 1000=9.25(101)+61.25 That would be 9.25*101=934.25+61.25=$995.50 Even though it does not equal $1000 it doesn't go over the budget and it very close to 1000. So 101 students can attend at the party if you pay $1000 and you will have $4.50 leftover. Also the number of students can't be a fraction or a decimal because there is no "half" person there can only be whole numbers.

## Purpose Plan:

## Bounce House- Hoppin Around Offers:

- 12 Variety of bounce houses/obstacle course
- 100 sq. ft. bounce house
- 100 ft. long obstacle course
- $75 per hour

## Hopin Around- Equation, Table, and Graph

## Bounce House- Jumpin Jacks Offers:

- 100 sq.ft. bounce house
- 100 ft. long obstacle course
- $54 per hour
- $84 fee

## Jumpin Jacks- Equation, Table, and Graph

## Critical Thinking Questions: Describe how you created each equation.

**Hoppin Around**- To start the equation you always have a total amount of money spent which is the y value (y=) Then you want to find the rate of change or how much you pay per hour. (y=75x) The x value represents the hours and now we find the y intercept which is the fee. Since there is no y intercept our equation is y=75x.

**Jumpin Jacks- **Like I said before, you always have your total amount of money you spend (y=). Then you find the rate of change or how much you spend per hour. (y=54x) then you find the y-intercept or the fee. (y=54x+84) so our equation is y=54x+84

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

Yes, there will be. As you saw in the table the 4th hour had a total of $300. I knew this because if you plug in the same x value your y value will equal the same.

**Hoppin Around- **y=75(4)=300

**Jumping Jacks- **y=54(4)=216+84=300

## If you have $750 how many hours can you have for the money your spending?

**Hoppin Around- **You need the equation to help you figure this problem out. We know the y value. (750=75x) We need to plug in the x to make it be the y value. So 75(10)= 750. So you can spend 10 hours on the bounce house for $750.

**Jumpin Jacks- **We already have the y value. (750=54x+84) We need to find an x value where the y value equals 750 or less but close. Lets try 12. (750=54(12)+84 So 54*12=648+84= $732. For Jumpin Jacks you can bounce for 12 hours and you save $18!

You can not have half an hour because the question asked for hours only so that would only be whole numbers.