PROBLEM SOLVING

Substitution

Learn the reliable method for substitution, then apply it to 11+ exam-style questions.

1 · WHAT YOU NEED TO KNOW

The idea

Algebra uses letters to represent numbers and relationships.

Picture itFollow what happens to the unknown
2 · THE METHOD

Follow these steps

  1. Translate the rule or wording into an expression.
  2. Substitute known values carefully, using brackets for negative values.
  3. Simplify in the correct order and check the result against the original relationship.
3 · WORKED EXAMPLES

See the method in action

Example 1

A bakery predicts its cumulative sales using the formula 5 + 7d, where d is the number of days since opening. How many items does the formula predict after 10 days?

  1. Substitute d = 10: 5 + 7 × 10 = 5 + 70 = 75.
Answer: 75
Example 2

A bakery predicts its cumulative sales using the formula 6 + 4d, where d is the number of days since opening. How many items does the formula predict after 15 days?

  1. Substitute d = 15: 6 + 4 × 15 = 6 + 60 = 66.
Answer: 66
4 · ELEVENSPRINT TIP

A useful shortcut

Simplify in the correct order and check the result against the original relationship.

5 · COMMON MISTAKES

Watch out for these

6 · TRY IT YOURSELF

Three fresh questions

Ready to check the method? You will get three fresh, validated questions.