In this activity, you will look at how to create formulas by deciding what types of expenses are involved in a party!

One great way to look at patterns is to look at hosting a party. What do you have to do in order to have a party? How much is the party going to cost? What are you going to buy? A lot of these questions depend on how many people are coming to the party.

There are some things that you are going to have to buy or even rent! If you have the party in a rented hall, you have to pay for it before the party even starts, and the price will be the same if 10 friends come or 100 friends show up.

You can create a formula to figure out just how much your party is going to cost. You can use algebra to figure out the answer.

For example, assume you have rented a hall. The cost of the hall and a few decorations for one night is about $400. Each person that shows up will eat and drink about $15 worth of groceries.

Use this formula:

C = 400 + 15p

C is the total cost

p is the number of people

Now figure out what the cost of the party will be if 10, 20, or 40 people show up. Do this by substituting in the number of people for p in the equation to get:

C = 400 + 15(10)
C = 400 + 150
C = $550 for 10 people

It's that easy! Now let's figure out how much the party will cost if you invite 20 or 40 people!

C = 400 + 15(20)
C = 400 + 300
C = $700 for 20 people

C = 400 + 15(40)
C = 400 + 600
C = $1,000 for 40 people

By using a formula to help plan the party, you can make sure that you don't invite too many people so you don't go over budget!

Now you try it! Using the same example as above, find out how much it would cost if 60 people came to your party. What would your formula look like?

  Self-check!