I have 2 hexagons with a ratio of similarity of 3/4. If I have 3a+b and a+2b, what is a/b?
since you neglected to give the diagram, i will assume that the relationship is meant to be:
$\displaystyle (3a + b) \mbox { : } (a + 2b) = 3:4$
$\displaystyle \Rightarrow \frac {3a + b}{a + 2b} = \frac {3}{4}$
$\displaystyle \Rightarrow 12a + 4b = 3a + 6b$ ...........i cross-multiplied
$\displaystyle \Rightarrow 9a - 2b = 0$
dividing through by b (since i'm confident it's not zero, as the ratio given won't work if it was), we get:
$\displaystyle \frac {9a}{b} - 2 = 0$
$\displaystyle \Rightarrow \frac {a}{b} = \frac {2}{9}$