# Planning A Party

### By: Mychal Iliff

I have decided that the 7th grade deserves a huge party at the end of the year to reward them for all of their hard work. However, rather than make all the decisions myself, I felt that it would be better for seventh graders to make the decisions on what types of things would make a great party. I have compiled a list of different activities that have worked well in the past, and have found some pricing for various companies that offer these activities.

Unfortunately, I have not gotten around to comparing any of these prices yet or calculating which one would be best. I am not sure how long this party will last, so I would like to have a range of times to choose from. I am also not sure how many of our 7th grade students will be participating in this party, so I need pricing for various numbers of students. As I know you have studied patterns, equations and rates of change so far this year, I know you will be able to help plan a spectacular party.## Part A – Grab some Grub

**Critical Thinking Questions**

**1.** **Describe how you created each equation. **

I used the formula Y=Mx+B and I plugged in the numbers on the poster to their correct variables. Then I solved each equation because of the independent Variable X, given to me from the table.

**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.**

If you work from 0 people on the table, up to (really any number)10 people, you will find that both tables are not the same. You can add 10 people each time until you have both graphs at the same number of people. I found that 55 people, on both tables, have a total of $570.00. Also, once your graph is created, you can find the general area of which the two points meet. Then either add or subtract from that point depending on where the points are located.

**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?**

If you had a budget of $1000 for Burger Bonanza, then only 98 students could attend. You can make the 1000 into a fraction by putting 1000/1 or you could make it a decimal by putting 1000 and adding a decimal point. 1000.00 If you had a budget of $1000 for Pizza Palace, then only 101 students could attend.

**Proposed Plan: **

Mr. Jones should use Burger Bonanza because the amount for one person at Burger Bonanza is less than the amount for one person at Pizza Palace. I chose the points (50,520.75) for Pizza Palace and (50,520) for Burger Bonanza. I found the unit rate for each and Burger Bonanza was 10.40/1 and Pizza Palace was 10.48/1. It was an 8 cent difference! An example would be X=10. The equation would be Y= 10.40 x 10+ 0. The answer to Y would be 104. Because the amount of money for one person was less with Burger Bonanza than Pizza Palace, Mr. Jones should chose Burger Bonanza.

## Part B- Bounce House

**Critical Thinking Questions**

**1. ****Describe how you created each equation**

I used the Information on the Posters to find, X- Rate of Change and B- the Y-intercept. I plugged the information of X and B into the equation Y= M x+B, and then I filled out the table knowing the equation.

**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.**

There will be a number of hours where both companies will cost the same. Both companies intercept at 4 hours and $300 dollars. I used the graph I made to determine the point of interception and both of the graphs landed on (4, 300). Then I went back and filled in 4 as X and I got $300.00.

**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?**

If you had a budget of $750.00, then the maximum amount of hours at Hoppin' Around is 10 Hours at $750.00 . The maximum amount of hours for Jumpin' Jacks is 12 hours at $732.00. To check, I plugged in the numbers to the equation. I already knew based off of my table the 10 hours is $750 for Hoppin' Around, so all I needed to solve was the hours you could have with $750 at Jumpin' Jacks. Once I plugged in my independent variables into the equation, I solved to see which number was closest to $750, but not over it. my answer as 12. They can both be turned into fractions and decimals.

**Proposed Plan: **

Mr. Jones should use Hoppin' Around because it is less expensive per person than Jumpin' Jacks is per person. I chose the two points (2, 192) and (2, 150). Then, after they I put them into fraction form, I found their unit Rates. Hoppin' Around's unit rate was $75/1 and Jumpin' Jacks unit rate was $96/1. Mr. Jones can save $21.00 per person. An example would be if X=5 people. The equation would be Y= 75 x 5+0. Y would equal $375 dollars per 5 people . Because.Because the amount of money for one person was less with Hoppin' Around than Jumpin' Jacks, Mr. Jones should chose Hoppin' Around.