Grade 8-9

5-Step Equation Substitution Strategy

Brian is 15 years older than Alice.  The sum of their ages is 83.  How old is Brian?

1. What do you know?

-  Define your variables 

- State facts and needed formulas

-  Use equations to relate your variables to each other based on statements given

Let a represent Alice's Age
Let b represent Brian’s age

Brian is 15 years older than Alice.  b = a + 15

The sum of their ages is 83.   a + b = 83

2. Substitute to create an equation with one variable

            - Simplify the equation by distributing and gathering like terms if necessary

  Substitute (a + 15) in for b.
a + (a + 15) = 83      

simplifies to

2a +15 = 83 

           

3. Solve your equation

            - Show each step clearly

  2a +15 = 83

       - 15   - 15          Subtract 15 from both sides

           2a = 68

2a = 68                 Divide both sides by 2

2       2

a = 34

4. Check your work

            - Substitute your answer into the original situation

            - Does it work?

           

If Alice is 34 years old then Brian is 34 + 15 = 49 years old.

34 + 49 = 83   Bingo Bango!

5. State your answer

            - Use proper language and sentence structure

            - Make sure you are answering the question asked

Brian is 49 years old.