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Word problems involving tickets and total costs are a common feature in GCSE Maths exams. They test your ability to set up and solve equations, as well as your understanding of basic arithmetic. The cinema ticket problem above is a great example. Let’s compare the correct method with a common mistake in table form:
| Step | Correct Method | Common Mistake |
|---|---|---|
| 1. Set up the equation | Let x be the number of child tickets. | Assume all tickets are adult or child tickets. |
| 2. Calculate adult cost | adults × £5 = £20 | Ignore the adult ticket cost. |
| 3. Write total cost | Total cost: 20 + 4x = 48 | Set up 5x = 48 or 4x = 48 |
| 4. Solve for x | 4x = 48 - 20 = 28 \implies x = 7 | x = 48/5 = 9.6 or x = 48/4 = 12 (not possible) |
| 5. Final answer | Mrs Adams bought 7 child tickets. | Incorrect answer, not matching the context of the problem. |
The key is to account for the cost of the adult tickets first, then use the remaining amount to find the number of child tickets. A common mistake is to divide the total amount by the price of one type of ticket, which ignores the mixed ticket prices.
If you find these types of word problems challenging, GCSE Maths Tuition can help you develop a step-by-step approach, ensuring you understand how to set up and solve equations correctly.
In summary, always break down the problem, account for all parts, and check your answer makes sense in the context. This method will help you tackle a wide range of similar questions with confidence.
