Helen and Ivan Question: Simplest Solution Explained
Corey CrossUnderstanding the Helen and Ivan Question
The Helen and Ivan question is a popular problem-solving exercise typically seen in exams like the PSLE Maths or similar problem-solving questions in GCSE Maths. These types of questions challenge students to apply logical reasoning and basic arithmetic to arrive at a solution. In this article, we break down the problem step-by-step, offer practical examples, and provide exam tips suited for UK qualifications like GCSE and A-Level Maths.
What Is the Helen and Ivan Question?
The Helen and Ivan question involves two characters, Helen and Ivan, who each have a different number of coins or items. For example:
Helen has 48 coins, while Ivan has 120 coins. Helen gives some coins to Ivan until they both have an equal number of coins. How many coins did Helen give Ivan?
This problem requires an understanding of basic operations like addition, subtraction, and the concept of equal distribution.
Step-by-Step Solution
Let’s solve the example step-by-step:
- Calculate the total number of coins: Helen has 48 coins, and Ivan has 120 coins. Together, they have 48 + 120 = 168 coins.
- Divide the coins equally: To distribute equally, divide the total number of coins by 2. 168 ÷ 2 = 84. Each person should have 84 coins.
- Determine how many coins Helen needs to give Ivan: Ivan already has 120 coins, but he needs to end up with 84 coins. Helen must give Ivan enough coins to bridge the gap. Calculate the difference: 120 - 84 = 36 coins.
Therefore, Helen needs to give 36 coins to Ivan.
Alternative Examples
Let’s try a few variations to practise:
| Helen's Coins | Ivan's Coins | Total Coins | Coins Each | Coins Helen Gives |
|---|---|---|---|---|
| 60 | 80 | 140 | 70 | 10 |
| 50 | 90 | 140 | 70 | 20 |
| 100 | 40 | 140 | 70 | 30 |
Exam Technique Tips
Here are some tips to tackle similar questions in UK exams:
- Read carefully: Ensure you understand the question fully before attempting a solution.
- Break down the problem: Divide the problem into smaller, manageable steps like calculating totals and differences.
- Check your work: After solving, review your calculations to ensure accuracy.
- Practise similar questions: Familiarise yourself with variations of the problem to build confidence.
Practice Exercises
Try solving these practice problems:
- Helen has 72 coins, and Ivan has 108 coins. How many coins should Helen give to Ivan?
- Helen has 35 coins, and Ivan has 55 coins. How many coins does Helen need to give Ivan for them to have an equal number?
- Helen has 120 coins, and Ivan has 80 coins. How many coins should Helen give Ivan?
Check your answers using the step-by-step method detailed above!
Why Practise Helen and Ivan Questions?
These types of questions develop essential problem-solving skills, such as:
- Logical reasoning: Understanding how to balance quantities.
- Arithmetic skills: Applying addition, subtraction, and division.
- Exam readiness: Building familiarity with real-world problem-solving scenarios.
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