Adding Nadia and the Ribbon Division Problem

Adding Nadia, a renowned problem solver, often takes on challenges involving the division of items into proportional pieces. Here’s a classic example involving a ribbon that is 48 inches long. The problem involves dividing the ribbon into two pieces, where one piece is three times as long as the other. This article will guide you through the process of solving this problem, using mathematical principles and algebraic equations. By the end of this discussion, you will understand how to find the lengths of each piece when given a total length and a ratio of division.

Understanding the Problem

The first step in solving any problem is understanding the given information and the goal. In this case, Nadia is given a 48-inch ribbon to be cut into two pieces, where one piece is three times as long as the other.

Setting Up the Equation

To begin solving the problem, we introduce a variable to represent the length of the shorter piece of ribbon. Let x represent the length of the shorter piece in inches. Consequently, the longer piece is three times as long, so it can be represented as 3x.

Solving the Equation

Given that the total length of the ribbon is 48 inches, we can set up the following equation:

x 3x 48

This simplifies to:

4x 48

To find the value of x, we divide both sides by 4:

x 48 / 4 12

Therefore, the shorter piece of ribbon is 12 inches long. The longer piece, being three times the length of the shorter piece, is:

3x 3 * 12 36 inches

Thus, the ribbon can be divided into a shorter piece of 12 inches and a longer piece of 36 inches.

Alternative Methods

There are different methods to solve problems of this nature, and this scene also illustrates some of them. Another way to approach the problem is by considering the ratio of the pieces. The ratio of the strings can be represented as 3:1. Knowing the total length, we can calculate the length of one piece by dividing the total length by the sum of the ratio parts.

Total Length / (3 1) 112 / 4 28 inches (shorter piece)

The longer piece is:

Total Length / (1) 112 * (3/4) 84 inches (longer piece)

Conclusion

By following step-by-step mathematical reasoning, we have successfully solved the problem of dividing a 48-inch ribbon into two pieces, one being three times as long as the other. This problem-solving technique can be applied to a variety of similar problems, such as dividing a quantity or length in a given ratio. Understanding and applying algebraic equations are crucial in solving such problems effectively.