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The points A, B, C and D lie in order on a straight line - Edexcel - GCSE Maths - Question 12 - 2017 - Paper 3

Question 12

The points A, B, C and D lie in order on a straight line. AB : BD = 1 : 5 AC : CD = 7 : 11 Work out AB : BC : CD

Worked Solution & Example Answer:The points A, B, C and D lie in order on a straight line - Edexcel - GCSE Maths - Question 12 - 2017 - Paper 3

Step 1

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Answer

Let AB be represented as x. Then, according to the ratio, BD can be expressed as 5x. Hence, the total length AD becomes:

$AD = AB + BD = x + 5x = 6x$

Step 2

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Answer

Using a similar approach, let AC be represented as 7y and CD be represented as 11y. Therefore, the total length AD can also be expressed as:

$AD = AC + CD = 7y + 11y = 18y$

Step 3

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Answer

Since both expressions for AD are equal, we can set them up as:

$6x = 18y$

Dividing both sides by 6 gives:

$x = 3y$

Now we can express AB, BC, and CD in terms of y:

Thus, we can now express the ratios as:

$AB : BC : CD = 3y : 4y : 11y$

Simplifying this gives:

$AB : BC : CD = 3 : 4 : 11$

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