# 7th Grade End of Year Bash

## Questions

1. Describe how you created each equation.

For each equation I took the provided number and placed them into the y=mx+b equation format. First I took the price per person and put it into the m slot. Then I took the set up fee and placed that into the b slot, and this gave me y=10x+20 and y=9.25x+61.25.

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.

For a situation like this, I would find the point of intersection. I do this by solving for where the x coordinate point would be where the two companies cross over. For the food, when there is 55 kids at the party, it costs \$570 for both of the companies. This is also known as the point of intersection.

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 you could have 98 people and for Pizza Palace you could have 101 people. You could not have a decimal or fraction as an answer because you couldn't have 1/3 of a person show up and 2/3 of themselves stay at their house.

## Activities

1. Describe how you created each equation.

I took the numbers from the posters and made them into the equations, which is y=mx+b, and one of them was just y=mx, with no y-intercept. The one with no y-intercept was Hoppin' Around, as it was just \$75 an hour. Jumpin' Jack's was different, as it had a y-intercept of \$84. They had a rate of \$54 per hour. These would come to equal y=75x for Hoppin' Around and y=54x+84 for Jumpin' Jack's.

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.

I would use the two equations to solve for what x would equal between the two. In this situation, it would be 4 hours. Your next step would be to plug that 4 into one of the equations, and the y would end up equaling 300, and this is the point of intersection, so the point of intersection is 4, 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?

For Hoppin' Around you would get 10 hours and with Jumpin' Jack's you would get 12 1/3 hours. You can use a decimal or fraction because this can be represented in time, as 1/3 of an hour is 20 minutes.

## Proposed Plans

Food-For the food, if there is more than 55 students at the 7th grade party, Pizza Palace is the way to go. If there is less than 55 students, I would go with Burger Bonanza. 55 is the point of intersection, so at this point it would cost the same amount for each one of these, at \$570.

Activities-For activities, if there is more than 4 hours of partying, Jumpin' Jack's would be the company for the party. If there is less than 4 hours, Hoppin' Around would be better. The 4 is important because that is the point of intersection, and if the party is this long, it will cost \$300 for each one of the companies