a piece of wire 80 inches long is cut into two pieces. one piece is 5 inches more than twice the other. how long is the shorter piece?

Let the length of the shorter piece be \( x \) inches. Then, the length of the longer piece will be \( 2x + 5 \) inches (since it is 5 inches more than twice the shorter piece).

The total length of the wire is 80 inches, so we can write the equation:

\[
x + (2x + 5) = 80
\]

Now, solve for \( x \):

\[
x + 2x + 5 = 80
\]
\[
3x + 5 = 80
\]
\[
3x = 80 - 5
\]
\[
3x = 75
\]
\[
x = \frac{75}{3} = 25
\]

Thus, the shorter piece is 25 inches long.

Would you like a detailed breakdown of the solution or have any questions?

Here are some related questions to expand your understanding:
1. What is the length of the longer piece in this situation?
2. How would the equation change if the longer piece were 10 inches more than twice the shorter piece?
3. What if the wire were cut into three pieces with specific length relationships?
4. Can this method be used for solving similar problems involving different total lengths?
5. How would this approach change if the total length were given in centimeters?

**Tip:** Always define variables clearly when setting up equations based on word problems. This helps in translating the problem accurately into mathematical terms.

A piece of wire 80 inches long is cut into two pieces. One piece is 5 inches more than twice the other. How long is the shorter piece?

Learn how to solve a linear equation problem where a piece of wire 80 inches long is cut into two pieces. One piece is 5 inches more than twice the other. This problem involves key algebraic concepts and is suitable for students in Grades 6-8.

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