   SEARCH HOME Math Central Quandaries & Queries  Question from Cynthia, a student: How do I solve this problem? A ten- foot long board is cut into three pieces. The second piece is half as long as the first. The third piece is 4 1/2 longer than the second. How long is the first? Hi Cynthia,

You need to set up an equation to solve for this problem and the first step is to decide which of the three lengths to be the variable. The problem tells you a relationship between the lengths of the first and second piece and then a relationship between the lengths of the second and third pieces. Since the second piece is mentioned in both these relationships I would let the variable be the length of the second piece.

Let the length of the second piece be x feet.
Now consider the two statements:

The second piece is half as long as the first.
Hence the first piece is 2x feet long

The third piece is 4 1/2 longer than the second.
This statement is unclear to me. If it should say

The third piece is 4 1/2 times longer than the second.
then the length of the third piece is 5.5 times x feet.

The third piece is 4 1/2 times as long as the second.
then the length of the third piece is 4.5 times x feet.

Since the board is 10 feet long you have

2x + x + "the length of the third piece" = 10

Solve for x.

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.