Find A:B, if (2A+4B)/(2A-4B) =3/2
I start with 2A+4B=3A-6B...
Hello,Find A:B, if (2A+4B)/(2A-4B) =3/2
I start with 2A+4B=3A-6B...
(scratch what was there before)
You could just cross-multiply :
$\displaystyle 2(2A + 4B) = 3(2A - 4B)$
Then expand :
$\displaystyle 4A + 8B = 6A - 12B$
Simplify :
$\displaystyle 20B = 2A$
Simplify again :
$\displaystyle 10B = A$
Finally :
$\displaystyle 10 = \frac{A}{B}$
Does it make sense ?
which is fine as the numerator is one and a half times the denominator.
then $\displaystyle 2A-2A+4B=3A-2A-6B\ \Rightarrow\ 4B=A-6B$
$\displaystyle 4B+6B=A+6B-6B=A$
$\displaystyle 10B=A\ \Rightarrow\ 10=\frac{A}{B}\ \Rightarrow\ A:B=10:1$
Or...
$\displaystyle \frac{2A+4B}{2A-4B}=\frac{3}{2}\ \Rightarrow\ \frac{2(2A+4B)}{2A-4B}=3$
$\displaystyle \Rightarrow\ 4A+8B=3(2A-4B)\ \Rightarrow\ 4A+8B=6A-12B$
$\displaystyle 20B=2A$