Links to other topics
List of Formulas Anglish Index
Types of Story Problems Examples of Story Problems
Angles of Triangles

Relation Problems

A twelve foot board is cut such that one piece is three feet shorter than half the length of the other. Determine the length of each piece. The formula for this problem is unknown X factor + term = entity - a version of the general relational equation.

The factor and term for the short piece of board are given. The factor and term for the long piece are assumed to be 1 and 0 respectively. Assume that the length of the longer piece is the "unknown length", then

        short piece unknown length = long piece unknown length X factor - term
Since we know that the sum of the lengths of the two pieces must add up to the total length of the original board, we get
        long piece unknown length + short unknown piece length = total length
Substituting in the above formula for short piece length gives:
        long piece unknown length + long piece unknown length X factor - term = total length
Solving for unknown lengths gives:
        unknown length$ = (total length + term) / (1+factor)
and then
        length$ = unknown lenght$ X factor$ - term$;
Click to see the board table, the program, or the results.