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 21 - 2020 - Paper 3

To find the ratio in the equation:

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

First, we can rearrange this equation:

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

Next, we need to isolate x:

$x = \frac{7y + 20y^2}{6}$

Now we express the ratio x : y as:

$\frac{x}{y} = \frac{\frac{7y + 20y^2}{6}}{y} = \frac{7 + 20y}{6}$

This ratio can be simplified further. At this point, we observe that if y is a positive value, we can conclude that:

For simplicity, let y = 1:

$\frac{x}{y} = \frac{7 + 20(1)}{6} = \frac{27}{6} = \frac{9}{2}$

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