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?(1 point)

Question

Responses

Answer 1

Let's define the length of the shorter section as $x$ inches. Since one section of the string is 5 inches longer than the other, the length of the longer section can be expressed as $x+5$ inches.

According to the problem, twice the length of the longer section is equal to three times the length of the shorter section. This gives us the equation:

$$2(x+5)=3x$$

Now, let's solve this equation 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.

Answer: The shorter section is 10 inches long.