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?
Let x be the length of the shorter section.
Then the length of the longer section is (x+5).
Twice the length of the longer section is three times the length of the shorter section, so we have the equation 2(x+5)=3x.
Simplifying the equation, we get 2x+10=3x.
Subtracting 2x from both sides, we have 10=x.
The shorter section is 10 inches long.
Let's assume the length of the shorter section of the string is x inches.
According to the question, the longer section is 5 inches longer than the shorter section. So, the length of the longer section is x + 5 inches.
Twice the length of the longer section is three times the length of the shorter section. In equation form, this can be written as:
2 * (x + 5) = 3 * x
Simplifying the equation:
2x + 10 = 3x
To solve for x (the length of the shorter section), we can subtract 2x from both sides of the equation:
10 = x
So, the length of the shorter section is 10 inches.