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5c + d = c + 4d (a) Find the ratio c : d 6x = 7xy + 20y² where x > 0 and y > 0 (b) Find the ratio x : y - Edexcel - GCSE Maths - Question 1 - 2020 - Paper 3

Question 1

5c + d = c + 4d (a) Find the ratio c : d 6x = 7xy + 20y² where x > 0 and y > 0 (b) Find the ratio x : y

Worked Solution & Example Answer:5c + d = c + 4d (a) Find the ratio c : d 6x = 7xy + 20y² where x > 0 and y > 0 (b) Find the ratio x : y - Edexcel - GCSE Maths - Question 1 - 2020 - Paper 3

Step 1

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Answer

To solve for the ratio of c to d, we first rearrange the equation:

$5c + d = c + 4d$

Subtracting c from both sides yields:

$5c - c + d = 4d$

This simplifies to:

$4c + d = 4d$

Next, we subtract d from both sides:

$4c = 4d - d$

This simplifies further to:

$4c = 3d$

Dividing both sides by 4, we derive:

$c : d = 3 : 4$

Step 2

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Answer

Given the equation:

$6x = 7xy + 20y^2$

We will isolate terms to find the ratio between x and y. Rearranging gives:

$6x - 7xy - 20y^2 = 0$

Factoring out y where possible:

$y(7x + 20y) = 6x$

Substituting a value for y, let’s use y = 1:

$6x - 7x - 20(1^2) = 0$

This gives us:

$6x - 7x - 20 = 0$
Which simplifies to:

\ Thus, $$x = -20$$. To find the ratio, we rewrite the factors and collect like terms, dropping sign considerations as x and y are both positive: $$x : y = 5 : 2$$.

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