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?

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- Jan 25th 2008, 12:48 PMdonnagirlRatios 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? - Jan 25th 2008, 12:53 PMKrizalid
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.