A 30ft long board is cut into 2 pieces. The ratio of the lengths of the 2 pieces is 2:3. What is the length, to the nearest foot, of the shorter piece?
How can you conclude that it is 12?
For these problems, think always to set a constant.
You have a condition which says that the ratio of the lengths of the 2 pieces is 2:3.
So let $\displaystyle (x,y)=(2k,3k)$ be such lenghts. (Where $\displaystyle k$ is a positive constant.)
But you know that board's lenght is 30 ft, so $\displaystyle x+y=30,$ it means $\displaystyle 2k+3k=5k=30$ and $\displaystyle k=6.$
The rest follows.