# Planning a Party

## What are we doing?

In this project we are using our previous knowledge of equations and graphs, to see what would be the best deal for some food and for some fun. Lets get started!

## Grab some Grub!

Food is always a necessity to any party, but so is the price. You always want to find a good deal on the food your buying, and especially make sure your not getting ripped off!

So, since we have the option of buying from Burger Bonanza or Pizza Palace, we have to use linear equations to find the better buy.

## Bonanza Burgers vs. Pizza Palace

How did I create each of these equations?

- Well, for both places I had to create a linear equation to see which place would be the better buy. To do this, I looked at the cost for each place per person, ( my rate of change) and I also looked at what was the start up fee ( the y-intercept). For Bonanza Burgers, they charged \$10 per person and \$20 for a start up fee. So, put it all together and you get: y=10x+20. ( 10, your rate of change; or how much it cost per person, and 20, your y-intercept; or start up fee). For Pizza Palace the rate of change, or amount it cost per person would be \$9.25, and the y-intercept, or the start up fee would be 61.25.

Will there ever be a number of students where both companies will cost the same?( Place of Intersection)

Yes, at 55 people ordering, there will be the same total cost. Shown below is how to find the Point of Intersection.

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 were to buy from Bonanza Burgers, you would be able to have a maximum of 98 people at the 7th Grade Blow out. If you were to buy from Pizza Palace, 101 people would be able to come to the 7th Grade Blowout. From Pizza Palace, you really have a decimal for the amount of people able to come to the 7th Grade Blowout. But, one wouldn't put this as an answer, because humans can't be split into to decimals. So, no there can't be a decimal or a fraction as a part of your answer.

Purposed Plan

-So, now that we were able to find out the better buy we know which Food Caterer would be the better buy. If below 55 people came, the better buy would be at Burger Bonanza. If more than 55 people came, the better investment would be to buy from Pizza Palace. If exactly 55 people came, it wouldn't matter which business you bought from.

## Bounce House!

If you want to have a fun activity, bounce houses are always a good way to go. But like we learned with the food, their most of the time is a better deal. So reverting back to what we did earlier, we will use linear equations to find the better buy.

## Jumping Jacks vs. Hoppin' Around

How did I create these equations?

- To create these equations, I looked at the cost per person, and in this case, one y-intercept. For Jumping Jacks it cost \$54 per person, so that would become my rate of change. It then had a set up and removal fee of 84. That would be my y-intercept. After that, all you have to do is set the numbers in linear equation form. So, you would come out with the equation y=54x+84. For Hoppin' Around, your cost per person is \$75. That becomes your rate of change. Since this problem doesn't have a y-intercept, you can now set up your equation in linear equation format. Your equation would look like y=75x.

Will there ever be a number of students where both companies will cost the same?( Place of Intersection)

-Yes, at 4 hours rented, it would cost the same amount. We don't really have to do a lot of math to figure this out, because it already says it on our table. Although this won't always happen, it helpful when it does!

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 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 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 were to buy from Jumpin' Jacks, 16 people would be able to come to the 7th Grade Blowout. If you were to buy from the company Hoppin' Around, 13 people would be able to come to the 7th Grade Blowout. Like the last problem, both companies had decimals as the answer; but since people can't be split into decimals or fractions, we have to use whole numbers. So no, one can/t have a decimal or fraction as a part of an answer.

Purposed Plan

-Now we also have the better buy for which bounce house would be the better buy. If you were to rent below four hours, Hoppin' Around would be the best investment. If you were to rent above four hours, Jumping' Jacks would be the better buy. If you were to rent from exactly four hours, it wouldn't matter which bounce company you would buy from.