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
15 inches
15 inches
12 inches
12 inches
10 inches
10 inches
20 inches
20 inches
Let's assume that the length of the shorter section is x inches.
According to the given information, the longer section would be x+5 inches.
Twice the length of the longer section is three times the length of the shorter section, which can be written as:
2(x+5) = 3x
Simplifying the equation:
2x + 10 = 3x
Subtracting 2x from both sides:
10 = x
Therefore, the length of the shorter section is 10 inches.
Let's assume the length of the shorter section of the string is x inches. Since the longer section is 5 inches longer, its length will be x + 5 inches.
According to the given information, twice the length of the longer section is three times the length of the shorter section. So, we can set up the equation:
2(x + 5) = 3x
We can simplify the equation:
2x + 10 = 3x
Now, let's solve for x. Subtracting 2x from both sides of the equation:
10 = 3x - 2x
10 = x
So, the length of the shorter section of the string is 10 inches.