https://file.aiquickdraw.com/mathbot/file/1726016830688dbqulrzt.jpg

The problem asks to define a variable, write an equation, and solve for the lengths of two pieces of cable where one piece is 18 meters longer than the other, and the total length is 84 meters.

### Step 1: Define a Variable
Let:
- \( x \) be the length of the shorter piece of cable (in meters).

Since the other piece is 18 meters longer:
- The length of the longer piece = \( x + 18 \) meters.

### Step 2: Write an Equation
The total length of the two pieces is 84 meters. Therefore, the equation is:
\[
x + (x + 18) = 84
\]

### Step 3: Solve the Equation
1. Combine like terms:
   \[
   2x + 18 = 84
   \]
2. Subtract 18 from both sides:
   \[
   2x = 66
   \]
3. Divide both sides by 2:
   \[
   x = 33
   \]

Thus, the length of the shorter piece is 33 meters.

### Step 4: Find the Length of the Longer Piece
The longer piece is \( x + 18 = 33 + 18 = 51 \) meters.

### Final Answer
- The shorter piece of cable is 33 meters.
- The longer piece of cable is 51 meters.

### Solution in a Sentence:
The cable is cut into two pieces where one piece is 33 meters, and the other is 51 meters.

Would you like more details or have any questions?

---

Here are 5 related questions you could explore:
1. What if the total length of the cable were 100 meters instead of 84?
2. How would the equation change if the longer piece were only 10 meters longer?
3. Could you solve the problem using a different method, such as guess and check?
4. How would the problem change if the lengths were given in feet rather than meters?
5. What if the difference between the two pieces was unknown and needed to be found first?

**Tip:** When solving word problems, always define your variable clearly and double-check units (meters, feet, etc.) to avoid confusion.

A cable 84 meters long is cut into two pieces so that one piece is 18 meters longer than the other. Find the length of each piece of cable.

Learn how to solve a linear equation problem involving cutting a cable into two pieces, where one piece is 18 meters longer than the other. Step-by-step solution for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation