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 be such lenghts. (Where is a positive constant.)
But you know that board's lenght is 30 ft, so it means and
The rest follows.