# Math Help - ratios

1. ## ratios

I have 2 hexagons with a ratio of similarity of 3/4. If I have 3a+b and a+2b, what is a/b?

2. Originally Posted by sanee66
I have 2 hexagons with a ratio of similarity of 3/4. If I have 3a+b and a+2b, what is a/b?
what do the variables a and b represent?

3. ## ratios

3a+b is on one hexagon and a+2b is on the other

4. Originally Posted by sanee66
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:

$(3a + b) \mbox { : } (a + 2b) = 3:4$

$\Rightarrow \frac {3a + b}{a + 2b} = \frac {3}{4}$

$\Rightarrow 12a + 4b = 3a + 6b$ ...........i cross-multiplied

$\Rightarrow 9a - 2b = 0$

dividing through by b (since i'm confident it's not zero, as the ratio given won't work if it was), we get:

$\frac {9a}{b} - 2 = 0$

$\Rightarrow \frac {a}{b} = \frac {2}{9}$