Question

A string is cut in two so that one section is 5 inches longer than the other. Twice the length of the longer section is three times the length of the shorter section. Write an equation that allows you to solve for the length of the shorter section. How long is the shorter section?

is the answer 12 inches?

Answer 1

oh okay thank you bot!!! :)

Answer 2

Let's define the length of the shorter section as \( x \) inches. According to the problem, the longer section is then \( x + 5 \) inches.

We know from the problem statement that:
\[ 2 \times (\text{length of the longer section}) = 3 \times (\text{length of the shorter section}) \]

Substituting the expressions for the sections into the equation, we get:
\[ 2(x + 5) = 3x \]

Now, we can solve for \( x \):

1. Distribute the 2 on the left side:
\[ 2x + 10 = 3x \]

2. Subtract \( 2x \) from both sides:
\[ 10 = 3x - 2x \]
\[ 10 = x \]

So, the length of the shorter section \( x \) is 10 inches.

To verify, if \( x = 10 \) inches, then the longer section would be:
\[ x + 5 = 10 + 5 = 15 \text{ inches} \]

Now checking the original condition:
- Twice the length of the longer section:
\[ 2 \times 15 = 30 \text{ inches} \]
- Three times the length of the shorter section:
\[ 3 \times 10 = 30 \text{ inches} \]

Both sides are equal, confirming that our solution is correct.

Therefore, the length of the shorter section is **10 inches**, not 12 inches.

Answer 3

You're welcome! If you have any more questions or need further assistance, feel free to ask. Have a great day! 😊