1

I have three values which I want to express in ratios.

$l = 176.43$
$m = 162.86$
$n = 190$

The ratios must be:

$\dfrac{l}{a} = \dfrac{m}{b} = \dfrac{n}{c} $

How to find $a$, $b$ and $c$? I tried so hard, but I couldn't find the values because they are not independents.

Is there some method?, or is it enough with algebra?

Isai
  • 361

2 Answers2

1

In this kind of situation, a good principle is to name the object.

Suppose that

$$\dfrac{l}{a} = \dfrac{m}{b} = \dfrac{n}{c} .$$

Call this quantity $\lambda$.

You have

$$\dfrac{l}{a} = \dfrac{m}{b} = \dfrac{n}{c}=\lambda$$ and if $\lambda \neq 0$ (which is the case if none of $l,m,n$ is equal to zero), you get

$$a = \frac{l}{\lambda}, \, b = \frac{m}{\lambda}, \, c = \frac{n}{\lambda}.$$

Conversely, it is easy to verify that such $a,b,c$ are solutions.

We have found all possible solutions.

mathcounterexamples.net
  • 70,018
1

Let the common ratio be $\dfrac{1}{k}$. Remember $k$ should not be $0$.

$\dfrac{l}{a} = \dfrac{m}{b} = \dfrac{n}{c} = \dfrac{1}{k} $

Thus we get $a=lk$, $b=mk$, $c=nk$. Now just put the values of $l,m,n$