Final answer:
To determine the length of the shorter piece of a 164-inch pipe where one piece is three times longer than the other, we define the shorter piece as x and set up the equation x + 3x = 164, solving for x to find that the shorter piece is 41 inches.
Step-by-step explanation:
To find the length of the shorter piece when a 164-inch pipe is cut into two pieces, with one piece being three times the length of the other, we can use the concept of algebra. Let's define the length of the shorter piece as x inches. Therefore, the longer piece will be 3x inches. The sum of both pieces should be equal to the total length of the pipe, which is 164 inches. We can write the following equation:
x + 3x = 164
Solving for x, we combine the like terms:
4x = 164
Now divide both sides by 4 to find x:
x = 164 / 4
x = 41
Therefore, the length of the shorter piece of the pipe is 41 inches.