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

Starting from the equation:

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

We can rearrange this by isolating all terms involving y on one side, we have:

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

Next, substitute a suitable value for y (for instance, let y = 1), we can solve for x:

Substituting y = 1 into the equation:

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

This simplifies to:

$6x - 7 - 20 = 0$

which leads to:

$6x - 27 = 0$

Thus:

$6x = 27 \\ x = \frac{27}{6} = \frac{9}{2}$

Now we have x and y as:

$x = \frac{9}{2}, \ y = 1$

Finding the ratio of x to y gives:

$\frac{x}{y} = \frac{\frac{9}{2}}{1} = \frac{9}{2}$

Therefore, the ratio x : y is 9 : 2.