Many GCSE questions present problems in words and expect you to form an equation, then solve it. This skill bridges real-world problems and algebra.
The Process
- Define the variable: let = the unknown quantity.
- Write the equation from the information given.
- Solve the equation.
- Check and interpret the answer in context.
Worked Example: Number Problem
Problem
"I think of a number, double it, and add 5. The result is 17. Find the number."
→ → .
Solution
Worked Example: Geometry Problem
Problem
"The angles in a triangle are , , and . Find ."
→ → →
Solution
Worked Example: Age Problem
Problem
"Tom is 5 years older than Sam. Their ages add to 31."
Let Sam = . Tom = . → → .
Sam is 13, Tom is 18.
Solution
Worked Example: Perimeter
Problem
"A rectangle has length and width . Perimeter = 34."
→ → → .
Length = 13, Width = 4.
Solution
Common Mistakes
- Not defining what represents.
- Setting up the equation incorrectly.
- Forgetting to check the answer in the original context.
Practice Problems
- Three consecutive numbers sum to 72. Find them.
- A rectangle's length is 3 times its width. Perimeter is 48. Find dimensions.
- Sarah has £. She spends £12 and has £23 left. Write and solve.
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Key Takeaways
Define variables clearly.
Translate words into algebra step by step.
Solve and check in the original context.