# Math Help - Ratios problem

1. ## Ratios problem

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?

2. 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 $(x,y)=(2k,3k)$ be such lenghts. (Where $k$ is a positive constant.)

But you know that board's lenght is 30 ft, so $x+y=30,$ it means $2k+3k=5k=30$ and $k=6.$

The rest follows.