Question
A 17-foot piece of string is cut into two pieces so that the longer piece is 5 feet longer than twice the shorter piece. If the shorter piece is x feet long, find the lengths of both pieces.
Question content area bottom
Part 1
The shorter piece is
enter your response here feet long.
The longer piece is
enter your response here feet long.
Question content area bottom
Part 1
The shorter piece is
enter your response here feet long.
The longer piece is
enter your response here feet long.
Answers
GPT-4o mini
Let's denote the length of the shorter piece as \( x \) feet. According to the problem, the longer piece is 5 feet longer than twice the shorter piece. Therefore, the length of the longer piece can be expressed as:
\[
2x + 5
\]
Since the total length of the string is 17 feet, we can set up the following equation:
\[
x + (2x + 5) = 17
\]
Now, let's simplify and solve for \( x \):
\[
x + 2x + 5 = 17
\]
Combining like terms, we have:
\[
3x + 5 = 17
\]
Next, subtract 5 from both sides:
\[
3x = 12
\]
Now, divide both sides by 3:
\[
x = 4
\]
So, the length of the shorter piece is \( 4 \) feet. Now we can find the length of the longer piece:
\[
2x + 5 = 2(4) + 5 = 8 + 5 = 13
\]
Thus, the lengths of both pieces are:
- The shorter piece: **4 feet**
- The longer piece: **13 feet**
**Answer:**
The shorter piece is **4 feet** long.
The longer piece is **13 feet** long.
\[
2x + 5
\]
Since the total length of the string is 17 feet, we can set up the following equation:
\[
x + (2x + 5) = 17
\]
Now, let's simplify and solve for \( x \):
\[
x + 2x + 5 = 17
\]
Combining like terms, we have:
\[
3x + 5 = 17
\]
Next, subtract 5 from both sides:
\[
3x = 12
\]
Now, divide both sides by 3:
\[
x = 4
\]
So, the length of the shorter piece is \( 4 \) feet. Now we can find the length of the longer piece:
\[
2x + 5 = 2(4) + 5 = 8 + 5 = 13
\]
Thus, the lengths of both pieces are:
- The shorter piece: **4 feet**
- The longer piece: **13 feet**
**Answer:**
The shorter piece is **4 feet** long.
The longer piece is **13 feet** long.