# Planning a Party Project

## Critical Thinking Questions (Part A)

Part A:

1. Describe how you created each equation. I created each equation by looking at the cost per person on each flyer and looked at any costly fees. I used the cost of people as my rate of change and the fees were my y-intercept for each individual food company. For the Burger Bonanza, it said it was a pricing of \$10 per person with an additional catering fee of \$20. So my equation is y (the total cost for the food) = 10x (\$10 per person) + \$20 (the additional catering fee). For Pizza Palace, it said the cost was \$9.25 per person with a setup fee of \$61.25. So my equation is y (the total cost for the food) = 9.25x (\$9.25 per person) + 61.25 (the setup fee).
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. To solve for the number of students for which both companies will cost the same, first, you set up the equations as algebraic expressions and make them equal to each other (expression 1 = expression 2). So for this situation it would be: 10x + 20 = 9.25x + 61.25. Then you solve for x.
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? For Burger Bonanza, the number of people maximum that they would be able to have at the 7th Grade Blowout, with a budget of \$1000 for food, is 98 people. For Pizza Palace, the number of people maximum that they would be able to have at 7th Grade Blowout, with a budget of \$1000 for food, is 101 people. You can't have a decimal or fraction as part of an answer because you can't have 0.486 of a person (as seen in the picture).

## Proposed Plan for Food

When solving for when the companies cost the same (point of intersection), I realized that on the graph that Pizza Palace costed more before they intersected at 55 people and that the Burger Bonanza costed less. After they crossed, Burger Bonanza costed more and Pizza Palace costed less. The proposed plan for the food is if there is less than 55 people then you should buy food from Burger Bonanza and if there is more than 55 people then you should buy food from Pizza Palace. If there is exactly 55 people then you can choose from Burger Bonanza or Pizza Palace.

## Critical Thinking Questions (Part B)

Part B:

1. Describe how you created each equation. I created each equation by looking at the cost per hour on each flyer and looked at any costly fees. I then used the cost per hour as my rate of change and the fees were my y-intercept for each individual bounce house company. For Hoppin’ Around, it said it cost \$75 per hour. So my equation is y (the total cost for the bounce house) = 75x (\$75 per hour). For Jumpin’ Jack’s, it said was \$54 plus an \$84 setup and removal fee. So my equation is y (the total cost for the bounce house) = 54x (\$54 per hour) + 84 (setup and removal fee).
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. To solve for the number of hours where both companies will cost the same, first, you set up the equations as algebraic expressions and make them equal to each other (expression 1 = expression 2). So for this situation it would be:
75x = 54x + 84. Then you solve for x.
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? For Hoppin' Around, the maximum hours they can have the bounce house at the 7th Grade Blowout, with the budget of \$750, is 10 hours. For Jumpin' Jack's, the maximum hours they can have the bounce house at the 7th Grade Blowout, with the budget of \$750, is 12 hours and 20 minutes. You can have a decimal or fraction as part of your answer because you can have 1/3 of a hour, which would be 20 minutes (as seen in the picture).

## Proposed Plan for Bounce House

When solving for when the companies cost the same (point of intersection), I realized that on the graph that Jumpin' Jack's costed more before they intersected at 4 hours and that the Hoppin' Around costed less. After they crossed, Hoppin' Around costed more and Jumpin' Jack's costed less. The proposed plan for the bounce house is if it is being used for less than 4 hours then you should buy the bounce house from Hoppin' Around and if it is being used for more than 4 hours then you should buy the bounce house from Jumpin' Jack's. If it is being used for exactly for 4 hours then you can choose from Hoppin' Around or Jumpin' Jack's.