ratios

**sfspitfire23** · July 26th 2010, 06:04 AM

Find A:B, if (2A+4B)/(2A-4B) =3/2

I start with 2A+4B=3A-6B...

**Bacterius** · July 26th 2010, 06:07 AM

Find A:B, if (2A+4B)/(2A-4B) =3/2
I start with 2A+4B=3A-6B...

Hello,
(scratch what was there before)

You could just cross-multiply :

$2(2A + 4B) = 3(2A - 4B)$

Then expand :

$4A + 8B = 6A - 12B$

Simplify :

$20B = 2A$

Simplify again :

$10B = A$

Finally :

$10 = \frac{A}{B}$

Does it make sense ?

**Also sprach Zarathustra** · July 26th 2010, 06:09 AM

2a+4b=3

&

2a-4b=2

**Archie Meade** · July 26th 2010, 06:35 AM

Originally Posted by sfspitfire23

Find A:B, if (2A+4B)/(2A-4B) =3/2

I start with 2A+4B=3A-6B...

which is fine as the numerator is one and a half times the denominator.

then $2A-2A+4B=3A-2A-6B\ \Rightarrow\ 4B=A-6B$

$4B+6B=A+6B-6B=A$

$10B=A\ \Rightarrow\ 10=\frac{A}{B}\ \Rightarrow\ A:B=10:1$

Or...

$\frac{2A+4B}{2A-4B}=\frac{3}{2}\ \Rightarrow\ \frac{2(2A+4B)}{2A-4B}=3$

$\Rightarrow\ 4A+8B=3(2A-4B)\ \Rightarrow\ 4A+8B=6A-12B$

$20B=2A$

**Bacterius** · July 26th 2010, 06:39 AM

Thanks Archie, for making me notice a typo in my post (fixed by the way). Enough math for me for today - too much mistakes.
Nice working also

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