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# Lesson 8 β Activity 1: Using Formulas to Find Missing Information

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# Lesson 8 β Activity 1: Using Formulas to Find Missing Information

#### Getting Ready

#### In the last lesson, you worked on creating formulas for patterns.

#### Try This:

#### Hereβs the example you looked at in L7 β A3:

#### Each term is multiplied by 25. This could be written as *tn* = 25*n*.

The eighth term was found by using this formula:

*t*8 = 25*n*

*t*8 = 25 x 8

*t*8 = 200

#### For a review, find the 12th term.

*t*12 = 25*n*

*t*12 = 25 x 12

*t*12 = 300

#### In this activity, you will use formulas to find missing information.

#### For example, let's say you are hosting a party and know it is going to cost $9 per person. You are not sure whether you want to invite 10 or 12 of your friends. The main problem is you only have a budget of $100 for the party. You could create a formula to help figure out how many friends you could invite.

#### Let's use the formula Total Cost (*T*) = 9 x number of friends invited (*f*):

__For 10 friends__: __For 12 friends__:

*T* = 9 x *f* *T* = 9 x *f*

*T* = 9 x 10 *T* = 9 x 12

*T* = $90 *T* = $108

__For 10 friends__:

__For 12 friends__:

*T*= 9 x

*f*

*T*= 9 x

*f*

*T*= 9 x 10

*T*= 9 x 12

*T*= $90

*T*= $108

#### So it will cost $90 to invite 10 friends and $108 to invite 12 friends. Since you only have $100 to spend, you can only invite 10 friends to your party.

#### What about if you were bringing cupcakes to school for your classmates? You want to bring two more cupcakes than the number of classmates you have in case the class has a visitor you didn't know about. There are 12 students in your shop class and 8 in your science class.

#### Let's use the formula Cupcakes (*C*) = number of students in your class (*n*)+2

#### For the shop class:

*C* = *n* + 2

*C* = 12 + 2

*C* = 14 cupcakes

#### For the science class:

*C* = *n* + 2

*C* = 8 + 2

*C* = 10 cupcakes

#### You need to bring 14 cupcakes to your shop class and 10 cupcakes to your science class. The nice thing about using a formula is that once you have it created, you can use it to solve for any missing number in a problem.

#### Let's go back to your party. A couple of your friends want the party to be bigger and are willing to help pay for the party. They want to invite 43 people in total. How much will the party cost now?

#### Use the formula you already have:

*T* = 9 x *f*

*T* = 9 x 43

*T* = $387

*T*= 9 x

*f*

*T*= 9 x 43

*T*= $387

#### The party will now cost $387.

#### It is much easier to use a formula to solve for many missing pieces of information in one problem than to solve for each piece individually.

#### Try This:

#### Write a formula and solve the following problem.

What if you were asked to bring cupcakes for the entire school?

There are 451
people in the school. Remember that you want to bring 2 extra just in
case somebody is visiting.

What if you were asked to bring cupcakes for the entire school?

There are 451 people in the school. Remember that you want to bring 2 extra just in case somebody is visiting.