7th Grade Party

By: Ivy Merrifield

Part A- Grab Some Grub

Describe how you created each equation.

To create each equation I set up y= and then I put the unit rate, 10/1, multiplied by x plus the flat rate of 20 dollars for Burger Bonanza.

For Pizza Palace I set it up the same way but with a unit rate of 9.25 and a flat fee of 61.25.

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.

Yes there will be a number where both companies will cost the same. It is called the point of intersection. To find the point of intersection I first had to find the x value. To find the x value I set up the equation 10x+20=9.25x+61.25 because they both equal y they equal each other. Then I did 10x-9.25xand got the equation .75x+20=61.25. After that I did .75x+20=61.25 61.25-20 to get .75x=41.25. Lastly I did .75x divided by .75 and 41.25 divided by .75 to end with a result of x=55. Then I plugged in x=55 to the equations and got the point of intersection as (55,570).

Proposed Plan:

I plan to go with Pizza Palace for three reasons. Reason 1 it is cheaper so there will be more money for other things at the party. Reason 2 everybody likes pizza I mean who have you met that doesn’t like pizza. Reason 3 we can have more people at the party and everyone can have a slice of pizza but if I went with Burger Bonanza only a couple of people would get a burger.

Part B- Bounce House

Describe how you created each equation.

To create each equation I set up y= and then I put the unit rate, 75/1, multiplied by x for Jumpin` Jacks.

For Hoppin` Around I set it up the same way but with a unit rate 54/1 of and a flat fee of 84.

Will there ever be a point in which the 2 companies numbers match? Describe the steps you would use and then solve for the number of hours for which both companies will cost the same amount.

Yes there will be a number where both companies will cost the same. It is called the point of intersection. To find the point of intersection I first had to find the x value. To find the x value I set up the equation 75x=54x+84 because they both equal y they equal each other. Then I did 75x-54x and got the equation 21x=84. Lastly I did 21x divided by 21 and 84 divided by 21 to end with a result of x=4. Then I plugged in x=4 to the equations and got the point of intersection as (4,300).

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 the budget was 750 dollars for a bounce house we could have only 10 hours for Jumpin` Jacks and 12 hours for Hoppin` Around.

Yes you can have a decimal or a fraction as an answer because you can have half of an hour and only pay for that half not the whole hour.

Proposed Plan:

I plan to go with jumpin` jacks because ido not think we will have a party that is over 2 hours. Jumpin` jacks will be cheaper for the party.

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 the budget was 1000 dollars for food we could have only 50 people for Burger Bonanza and 100 people for Pizza Palace.

No you cannot have a fraction or decimal as your answer because that would mean you would have a fraction or decimal of a person and that is not possible.