If the ratio of $a$ to $b$ is $3:2$ and the ratio of $btoc$ is $8:7$, what is the combined ratio of $a:b:c$?

We are given two separate ratios:
1. $a:b=3:2$
2. $b:c=8:7$

To combine them, we make the value of $b$ identical in both ratios. The lowest common multiple ($\text{LCM}$) of $2$ and $8$ is $8$.
Multiply the first ratio by $4$:

$$a:b=(3\times 4):(2\times 4)=12:8$$

Since the second ratio already has $b=8$, we can directly group them:

$$a:b:c=12:8:7$$