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 ?

Yes you can do that if you are only concerned with the answer and do not care much about the correctness and rigour of the method. — Shraddheya Shendre, Dec 22 '16 at 11:01

score 5 · Answer 1 · answered Dec 22 '16 at 11:06

5

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

answered Dec 22 '16 at 11:06

E.H.E

23,280

score 2 · Accepted Answer · edited Dec 22 '16 at 11:19

2

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

Thus,

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

edited Dec 22 '16 at 11:19

answered Dec 22 '16 at 11:17

Kanwaljit Singh

8,610

score 1 · Answer 3 · answered Dec 22 '16 at 11:01

1

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 $$ \frac y{x-y} = \frac{3a}{7a - 3a} = \frac{3}{7-3}= \frac 34. $$

answered Dec 22 '16 at 11:01

martini

84,101

score 0 · Answer 4 · answered Dec 22 '16 at 11:02

0

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

answered Dec 22 '16 at 11:02

Zestylemonzi

4,103

Yes.. thanks for the answer ! – Sunny Dec 22 '16 at 11:31

Fred · Answer 5 · 2016-12-22T11:15:50.573

0

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

edited Dec 22 '16 at 11:15

answered Dec 22 '16 at 11:05

Fred

77,394

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

5 Answers5