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)
Responses
12 inches
12 inches
10 inches
10 inches
20 inches
20 inches
15 inches
Let's let x be the length of the shorter section of the string.
According to the problem, the longer section is 5 inches longer than the shorter section, so we can represent this as (x+5).
The problem also states that twice the length of the longer section is three times the length of the shorter section. Mathematically, this can be written as 2*(x+5) = 3*x.
Simplifying this equation, we get:
2x + 10 = 3x
Subtracting 2x from both sides of the equation, we get:
10 = x
So the length of the shorter section, x, is 10 inches.
Let's denote the length of the shorter section as "x" inches. According to the given information, the longer section is 5 inches longer than the shorter section, so its length would be (x+5) inches.
Twice the length of the longer section is three times the length of the shorter section. Mathematically, we can represent this as:
2 * (x+5) = 3x
Simplifying the equation by distributing the 2 on the left side, we get:
2x + 10 = 3x
Subtracting 2x from both sides of the equation, we have:
10 = 3x - 2x
Combining the x terms on the right side, we get:
10 = x
So, the length of the shorter section is indeed 10 inches.