Lesson 8 — Activity 1: Using Formulas to Find Missing Information


Getting Ready



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


Try This:


Here’s the example you looked at in L7 — A3:


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


The eighth term was found by using this formula:
t8 = 25n

t8 = 25 x 8

t8 = 200


For a review, find the 12th term.

t12 = 25n
t12 = 25 x 12
t12 =  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

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.


You can use a formula to plan a 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.


You can use a formula for this next problem too.

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

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.

You can use a formula to plan a party.
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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.


C = n+2
C = 451 + 2
C = 453 cupcakes
 
You will have to bring 453 cupcakes.