A 96 m rope needs to be cut into 2 pieces, one of the pieces needs to be 3 times longer than the other.

Let the length of the shorter piece of rope be \( x \). The longer piece of rope is 3 times longer than the shorter one, so its length would be \( 3x \).

Given that the total length of the rope is 96 meters, we can express the sum of the two pieces as:

\[
x + 3x = 96
\]

Simplifying the equation:

\[
4x = 96
\]

Solving for \( x \):

\[
x = \frac{96}{4} = 24
\]

So, the shorter piece is 24 meters, and the longer piece is:

\[
3x = 3 \times 24 = 72 \text{ meters}.
\]

Thus, the shorter piece is 24 meters long, and the longer piece is 72 meters long.

Would you like more details or have any questions?

Here are 5 related questions:
1. What if the rope was 120 meters instead of 96 meters?
2. How would the equation change if the longer piece needed to be 4 times longer than the shorter one?
3. What if the total rope length and one of the pieces' lengths were known, and you needed to find the length of the other piece?
4. How would the solution differ if the total rope length were given in centimeters instead of meters?
5. What if the rope had to be cut into three pieces in a specific ratio?

**Tip:** Always set up equations that match the conditions described in the problem. This helps to systematically solve for unknowns.

Explore how to divide a 96 meter rope into two pieces where one piece is three times longer than the other. Step-by-step mathematical solution provided, covering equations and proportions. Suitable for students in Grades 6-8.

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