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 the length of the shorter section. How long is the shorter section?

Answer 1

Let's denote the length of the shorter section as \( x \) inches. According to the problem, the longer section is 5 inches longer than the shorter section, which means the length of the longer section can be represented as \( x + 5 \) inches.

The problem states that twice the length of the longer section is equal to three times the length of the shorter section. We can write this relationship as an equation:

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

Now, let's simplify and solve the equation:

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

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

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

In conclusion, the length of the shorter section is 10 inches.