If $x:y = 7:3$ , then find the value of $\frac{y}{x-y}$

Question

If $x:y = 7:3$ , then can I in order to find the value of $\frac{y}{x-y}$ replace $x$ and $y$ with $7$ and $3$ respectively ?

Answer 1

When we have some ratio, multiply it with some variable to find values. So let $x = 7z, y = 3z$.

Thus,

$$ \frac{y}{x-y} = \frac{3z}{7z - 3z} = \frac{3z}{4z}= \frac{3}{4}$$

Answer 2

Yes, you can. Note that $\frac xy = \frac 73$ gives you that for some $a \in \mathbf R$ we have $x = 7a$ and $y = 3a$, we then have $$ \frac y{x-y} = \frac{3a}{7a - 3a} = \frac{3}{7-3}= \frac 34. $$

Answer 3

Hint: What does ratio really mean? $x:y = 7:3$ represents that $x=\frac{7}{3}y$ can you continue from here?

Answer 4

$ \frac{x-y}{y}=\frac{x}{y}-1=\frac{7}{3}-1=\frac{4}{3}$. Hence, what you want $=\frac{3}{4}$

Answer 5

$$\frac y{x-y}=\frac 1{\frac{x}{y}-1}$$