# Planning a party

### by mike velisar

## Food

## How did you make the equation?

I knew that that the equation had to be in Y=mx+b form. To find b all I had to do is find the Y intercept which is the additional fee. On the flier it said that the additional fee was $20 so that was b. m was how much money they had to spend per person, which is $10. Now the Y=mx+b equation is Y=10x+20.

## How did you make the equation?

I again knew that the equation had to be in Y=mx+b form. To find b i looked in the flier to see the set up fee or the y intercept and i found that it was $61.25 so I plugged that in for b. To find m I had to find how much money the costumers payed per person. On the flier it said $9.25 per person. After I plugged that in for m the equation became Y=9.25x+61.25

## Will there ever be a number of students where both companies will cost the same?

Yes, they will be the same at 55 customers. First I needed to find where generally they would cost the same so I made a graph with both lines. I saw that it was a little higher than 50. Then I decided to plug in to my equations to see if I would get the same answer. I plugged in 50, 51, 52, 53, and 54 and they didn't work, but when I plugged in 55 I got 570 on both

Burger Bonanza:

Y=10 55+20= 570

Pizza Place:

Y=9.25 55+61.25= 570

## 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?

Burger Bonanza

98 people

Pizza Place

101 people

In this situation if I wanted to get the exact number I would have to use decimals. This would not be appropriate because you can not bring a fragment of a person.

## Plan

If there are less than 55 students coming choose Pizza Place, if there are more choose Burger Bonanza because you will get the cheapest price this way.

## Bounce House

## How did you make the equation?

I knew that normally the equation would be Y=mx+b but in this case there is no b because there is no added fee. This leaves the equation at Y=mx. Since now I know the form of the equation I just need to find the variable m. To find m I looked for how much each hour cost, and on the flier it said 75. Now that I know m my equation is Y=75x

## How did you make the equation?

Since the equation had to be Y=mx+b all I had to do was find m and b. To find b I looked for the additional fees. On the flier it said additional $84 for set-up and removal fee, so I put 84 for b. To find m I looked for the amount of money it cost per hour. I found that it was $54 so I put 54 for m. Now that I found my variables the equation was Y=54x+84.

## Will there ever be a number of hours where both companies will cost the same?

Yes, at 4 hours you will spend $300 on both bounce house companies. To find this all that I had to do was look at the graph and see that at 4 hours you would spend $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?

Hoppin' Around

10 hours

Jumpin' Jack's

12.33333333...

In this situation it is appropriate to add decimals because you can play a fraction of an hour.

## Plan

If you are going to use the bounce house for less than 4 hours get a bounce house with Hoppin' Around, but if you are planning on using it for more than 4 hours use Jumpin' Jack's to ensure that you get the best deal.