## Using Variables to Represent Two Quantities

#### Aligned To Common Core Standard:

**Grade 6 Expressions and Equations** - 6.EE.C.9

How to Use Variables to Represent Two Quantities In An Equation?
In sixth grade, the students learn to solve word problems that include the use of variables in them. By this time, the students have an idea about solving algebraic equations and calculating the value of the unknown variable.
A lot of kids find the variable word problems challenging and are scared to deal with them. However, these word problems are not that difficult, and the use of variables actually makes solving word problems simple and easy.
Example:
Alison and Ben have 50 cents in total. Alison has 10 cents more than ben. If ben's share is 20 cents, what is Alison's share?
**Step 1** - Create Sentences/Instructions
The first step is to highlight the keywords in the world problem and organize the data.
Alison's share+Ben's share=50
Alison's share=Ben's share+10
**Step 2** - Assume Variables
To make the word problem easy, you need to introduce variables into the solution.
Let Ben's share be "x."
Let Alison's share be "y."
**Step 3** - Incorporate Variables into Sentences Created
x+y=50
y=x+10
Step 4: Solve
As we know Ben's share, we can incorporate it into these equations and find out Alison's share;
y=20+10
Alison's share is 30 cents.
These worksheets and lessons will help students navigate one of the more tricker portions of the algebra curriculum. Students are asked to use two different variables in the same expression or equation.

### Printable Worksheets And Lessons

- Making Pastries Step-by-step
Lesson- The amount of math problems found in a kitchen never cease to amaze me.

- Guided Lesson - You start to have to play with two variable sets in this lesson.

- Guided Lesson Explanation - When you look at the problems the way I do here, they seem simple.

- Practice Worksheet - I tried to make these problems more about the setup than the actual calculations.

- Matching Worksheet - A nice way to wrap up the section. Clear cut problems.

#### Homework Sheets

This would be the first transition students make to using algebra in story based problems.

- Homework 1 - The equation below shows the number of cupcakes Garcia has made as it relates to the number of days she has spent making the cup-cakes. c = 5d The variable d represents the number of days spent making cup-cakes, and the variable c represents the number of cup-cakes.
- Homework 2 - The below equation represents how many pages are in a book that Eric is reading and how it depends on the number of pages he reads daily.
- Homework 3 - This equation shows how the total number of mosquitoes born is related to the number of days in a season.

#### Practice Worksheets

Playing cards start making an appearance here.

- Practice 1 - The variable r represents rounds, and the variable t represents the time taken to complete a round. How many rounds can he complete in a 5 minutes?
- Practice 2 - The equation shows how much furniture a carpenter makes as related to the number of days he has. f = 5d
- Practice 3 - The variable a represents ace cards, and the variable o represents other cards. How many ace cards are there if there are 48 other cards?

#### Math Skill Quizzes

I made everything in multiple choice format here to provide students a little bit of a prompt.

- Quiz 1 - The variable d represents dolls, and the variable w represents the number of days to make dolls. How many dolls can Rita make in a 5 days?
- Quiz 2 - The variable t represents total amount, m represents the number of mangoes and c represents the number of cucumbers. If John buys 12 items and 3 were mangoes, how many cucumbers did he buy?
- Quiz 3 - The above equation shows the time (min.) needed to bake a cake as related to the number of cakes being baked.