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.

Question

Write an equation that allows you to solve for the length of the shorter section.
How long is the shorter section?
A. 20 inches
B. 10 inches
C. 12 inches
D. 15 inches

Answer 1

Let the length of the shorter section be \( x \) inches. Then the longer section would be \( x + 5 \) inches.

According to the problem, twice the length of the longer section is equal to three times the length of the shorter section. We can express this relationship with the following equation:

\[ 2(x + 5) = 3x \]

Now, let's solve this equation:

1. Distribute the 2 on the left side:

\[ 2x + 10 = 3x \]

2. Subtract \( 2x \) from both sides:

\[ 10 = 3x - 2x \]

3. Simplify:

\[ 10 = x \]

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

The correct answer is:

B. 10 inches.

Answer 2

are you sure this is correct

Answer 3

Let's review the solution step by step to ensure accuracy.

1. Define the variables: Let \( x \) be the length of the shorter section. Then the longer section is \( x + 5 \).

2. Set up the equation based on the relationship provided:

   • Twice the length of the longer section (which is \( x + 5 \)) equals three times the length of the shorter section (which is \( x \)). This gives: \[ 2(x + 5) = 3x \]

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

4. Rearrange the equation: Subtract \( 2x \) from both sides: \[ 10 = 3x - 2x \] This simplifies to: \[ 10 = x \]

5. Conclusion: Thus, the length of the shorter section is \( x = 10 \) inches.

So, the earlier solution and reasoning are indeed correct. The length of the shorter section is 10 inches.

The answer is B. 10 inches.