Master the Supposition Method for Maths Success

What is the Supposition Method?

The supposition method is a powerful mathematical technique used to solve word problems, particularly those involving algebra, ratios, or percentages. It involves making an assumption (or supposition), solving based on that assumption, and then adjusting if necessary to find the correct solution. This method is commonly used in GCSE and A-Level exams, as it simplifies complex problems into manageable steps.

Why is the Supposition Method Useful?

This method helps students break down challenging word problems systematically. By assuming a value and working logically, it reduces confusion and provides clarity. It’s especially useful for problems where relationships between quantities are defined, such as:

• Ratio problems: Finding unknown quantities within given ratios.
• Percentage problems: Working with increases or decreases in value.
• Algebra problems: Solving equations where relationships between variables are stated.

How Does the Supposition Method Work?

Step-by-Step Explanation

Follow these steps to apply the supposition method effectively:

1. Read the problem carefully: Identify the key information, including relationships between quantities.
2. Make a supposition: Assume a value for one of the unknowns (e.g., let one item cost £1).
3. Solve based on the assumption: Use the relationships provided in the question to calculate the other unknowns.
4. Adjust if necessary: If the assumption leads to a contradiction or incorrect value, revise the assumption and repeat the process.

Practical Examples

Example 1: Ratio Problem

Question: The ratio of boys to girls in a class is 3:2. If there are 30 students in total, how many boys and girls are there?

Solution:

1. Supposition: Let the number of boys be 3x and the number of girls be 2x.
2. Equation: 3x + 2x = 30
3. Solve: Combine terms to get 5x = 30, then divide by 5 to find x = 6.
4. Substitute: Boys = 3x = 18, Girls = 2x = 12.
5. Answer: There are 18 boys and 12 girls.

Example 2: Percentage Problem

Question: A shop increases the price of a jacket by 20%. If the original price was £50, what is the new price?

Solution:

1. Supposition: Let the original price be £50.
2. Calculation: 20% of £50 = 0.2 × 50 = £10.
3. Add: £50 + £10 = £60.
4. Answer: The new price is £60.

Example 3: Algebra Problem

Question: A rectangle’s length is twice its width. If the perimeter is 60 cm, find the dimensions of the rectangle.

Solution:

1. Supposition: Let the width be x and the length be 2x.
2. Equation: Perimeter = 2(length + width) = 2(2x + x) = 60.
3. Solve: 2(3x) = 60 → 6x = 60 → x = 10.
4. Substitute: Width = x = 10 cm, Length = 2x = 20 cm.
5. Answer: The dimensions are 10 cm × 20 cm.

Practice Exercises

Test your understanding with these problems:

• Problem 1: The ratio of apples to oranges in a basket is 4:3, and there are 28 fruits in total. How many apples and oranges are there?
• Problem 2: A product's price increases by 15%. If the original price was £80, what is the new price?
• Problem 3: The length of a rectangle is three times its width. If the perimeter is 96 cm, find the dimensions of the rectangle.

Exam Tips for Using the Supposition Method

Here are some practical tips for GCSE and A-Level exams:

• Highlight key information: Underline ratios, percentages, or relationships in the question.
• Check your assumptions: If your solution doesn’t fit the question, revisit the supposition.
• Practise regularly: Familiarise yourself with common word problems using the supposition method.
• Write neatly: Clearly outline each step to avoid losing marks for working.
• Use time wisely: Don’t overthink. If stuck, move on and return to the problem later.

"The supposition method is a lifesaver for complex Maths questions. With practice, you’ll tackle problems with ease and confidence."

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