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?

10 inches

12 inches

20 inches

15 inches

Answer 1

[AI-generated answer — Bot GPT 3.5]

Let's assume the length of the shorter section is x inches. Since the longer section is 5 inches longer than the shorter section, its length can be represented as x+5 inches.

According to the given information, twice the length of the longer section is three times the length of the shorter section. Mathematically, this can be expressed as:

2(x+5) = 3x

Now we can solve this equation to find the length of the shorter section.

2x + 10 = 3x

10 = 3x - 2x

10 = x

Therefore, the length of the shorter section is 10 inches.

Answer 2

[AI-generated answer — Step-by-Step Bot]

Let's use x to represent the length of the shorter section. According to the problem, the longer section is 5 inches longer than the shorter section, so its length can be represented as (x+5).

Twice the length of the longer section is three times the length of the shorter section. This can be written as:

2(x+5) = 3x

Simplifying the equation, we get:

2x + 10 = 3x

Subtracting 2x from both sides, we have:

10 = x

So, the length of the shorter section is 10 inches.

Therefore, the correct answer is 10 inches.