## Prices

To get food there are two choices for catering, the two choices are Burger Bonanza and Pizza Palace. Burger Bonanza has an initial catering fee of \$20 along with \$10 per person. Pizza Palace has an set up fee of \$61.25 and \$9.25 per person.

## Food

1.)

To create the equations for the two catering businesses I first looked for the cost per person (K) and then the initial cost (B). Finally I placed the numbers in the y=kx+b formula.

2.)

Yes, eventually the two companies would come across a point of intersection. If you want ot invite 55 students then you can order from each company and have equal amounts.

3.)

With a budget of \$1000 you would only be able to invite 101 students you were ordering pizza. If you were ordering burgers then you would only be able to invite 98 students. Since you can't invite a fraction of a person you should NEVER have a decimal or fraction as your answer because it is unrealistic.

Proposed Plan:

If you want to invite 0-54 students then you would order catering from Burger Bonanza, but if you want an increased number of students (55+) to come then pizza should be ordered due to it's lower price after crossing the point of intersection (55 students/\$570) .

## Prices

For entertainment the school has chosen a bounce house. There are two businesses to choose from, Hoppin' Around which is \$75 an hour, or Jumping' Jack's which is \$54 an hour with the additional set up fee of \$84.

## Bounce House

1.)

I looked for the hourly rate for each bounce house company (k) and the additional set up fee {if any} (b), then plugged it into the formula y=kx+b

2.)

If the party is planned to be four hours than it will be \$300 for either company.

3.)

If we are given a budget of \$750 for the bounce houses than you would more likely want to rent from Jumpin' Jack's because you can have the house for 12 hours, rather than 10.

Proposed Plan:

If the party is planned to be 0-3 hours than you would want to rent from Bouncin' Around, but if the party is to last 4+ hours than you should rent from Jumpin' Jack's because once you have reached the point of intersection (4hrs./\$300) thats when this company becomes cheaper.