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Kiaria is 7 years older than Jay - Edexcel - GCSE Maths - Question 2 - 2017 - Paper 1

Question 2

Kiaria is 7 years older than Jay. Martha is twice as old as Kiaria. The sum of their three ages is 77. Find the ratio of Jay’s age to Kiaria’s age to Martha’s age.

Worked Solution & Example Answer:Kiaria is 7 years older than Jay - Edexcel - GCSE Maths - Question 2 - 2017 - Paper 1

Step 1

Let Jay's age be x

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Answer

We start by defining Jay's age as $x$ . Therefore, we can express Kiaria's age as:

$K = x + 7$

And since Martha is twice as old as Kiaria, we have:

$M = 2K = 2(x + 7)$

Step 2

Set up the equation for the sum of ages

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Answer

The sum of their ages can be expressed as:

$x + K + M = 77$

Substituting the expressions for $K$ and $M$ :

$x + (x + 7) + 2(x + 7) = 77$

Step 3

Simplify and solve for x

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Answer

Combining like terms, we get:

$x + x + 7 + 2x + 14 = 77$

This simplifies to:

$4x + 21 = 77$

Subtracting 21 from both sides gives:

$4x = 56$

Dividing by 4 results in:

$x = 14$

Step 4

Calculate the ages and the ratio

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Answer

We find Jay's age is $14$ , Kiaria's age is:

$K = 14 + 7 = 21$

And Martha's age is:

$M = 2(21) = 42$

The ratio of Jay's age to Kiaria's age to Martha's age is:

$\text{Ratio} = J:K:M = 14:21:42$

This can be simplified by dividing each term by 7:

$\text{Ratio} = 2:3:6$

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