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6(a) Given the ratio of two quantities in the form of $2 : 6 : 3$ - Edexcel - GCSE Maths - Question 6 - 2022 - Paper 1

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6(a) Given the ratio of two quantities in the form of $2 : 6 : 3$. Express the ratio in simplest form. 6(b) Express all numbers in terms of one number. If... show full transcript

Worked Solution & Example Answer:6(a) Given the ratio of two quantities in the form of $2 : 6 : 3$ - Edexcel - GCSE Maths - Question 6 - 2022 - Paper 1

Step 1

Express the ratio in simplest form.

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Answer

To simplify the ratio 2:6:32 : 6 : 3, we first look for the greatest common divisor (GCD) of the numbers involved. The GCD of 2, 6, and 3 is 1. Therefore, the ratio is already in its simplest form as 2:6:32 : 6 : 3.

Step 2

Express all numbers in terms of one number.

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Answer

Given the equation x=ax = a, we can express the other variables as follows:

  1. For bb, we can derive that b=23ab = \frac{2}{3}a.
  2. For cc, we can find that c=32ac = \frac{3}{2}a.
    Thus, the expressions in terms of the variable aa are:
  • b=23ab = \frac{2}{3}a
  • c=32ac = \frac{3}{2}a.

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