Solving a Real-World Problem: Cutting a 73-metre Pole into Two Lengths

Your task today is to solve a practical mathematical problem. Imagine you have a pole that is 73 meters in length. This pole needs to be cut into two pieces such that the longer piece is 16 meters longer than twice the length of the shorter piece. Let's break down the problem step-by-step.

Understanding the Problem

Let's denote the length of the shorter piece of the pole as x meters. The problem states that the longer piece is 16 meters longer than twice the length of the shorter piece. This gives us the following expression for the length of the longer piece:

Longer piece 2x 16

Since the total length of the pole is 73 meters, we can set up the following equation:

x (2x 16) 73

Solving the Equation

Let's simplify the equation step-by-step.

Combine like terms: x 2x 16 73 3x 16 73

Now, let's isolate the variable x by following these steps:

Subtract 16 from both sides of the equation: 3x 73 - 16 3x 57

Next, divide both sides by 3 to solve for x:

x 57 / 3

x 19

Therefore, the length of the shorter piece is 19 meters.

Finding the Length of the Longer Piece

Now that we know the length of the shorter piece, we can find the length of the longer piece:

Longer piece 2x 16

Substitute x with 19:

Longer piece 2(19) 16

Longer piece 38 16

Longer piece 54 meters

Verification

To ensure our solution is correct, let's check the total length:

Shorter piece Longer piece 19 54

19 54 73 meters (which matches the initial length of the pole)

Thus, the lengths of the two pieces are:

Shorter piece: 19 meters Longer piece: 54 meters

Conclusion

In this article, we solved a practical algebraic problem involving the division of a 73-meter pole into two pieces with specific conditions. By breaking down the problem and systematically solving the equation, we found the lengths of both pieces. This type of problem-solving can be applied in various real-world scenarios, such as in construction, woodworking, and even in everyday situations where equal or proportional distribution is required.

To reinforce your understanding, you can practice similar problems or explore more complex algebraic equations in your studies.