The ratio $(y + x):(y - x)$ is equivalent to $k:1$ - Edexcel - GCSE Maths - Question 14 - 2017 - Paper 1
Question 14
The ratio $(y + x):(y - x)$ is equivalent to $k:1$.
Show that $y = \frac{x(k + 1)}{k - 1}$.
Worked Solution & Example Answer:The ratio $(y + x):(y - x)$ is equivalent to $k:1$ - Edexcel - GCSE Maths - Question 14 - 2017 - Paper 1
Step 1: Set up the ratio
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Starting from the given ratio, we can express it as:
y−xy+x=1k
This implies that (y+x)=k(y−x).
Step 2: Rearrange the equation
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Expanding the right side, we have:
y+x=ky−kx
Rearranging terms gives:
y−ky=−kx−x
which simplifies to:
y(1−k)=−x(k+1).
Step 3: Solve for y
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To isolate y, divide both sides by (1−k) (assuming k=1):
y=1−k−x(k+1).
This simplifies to:
y=k−1x(k+1), as required.
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