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 sections. How long is the shorter section.
a. 10 inches
b. 12 inches
c. 20 inches
d. 15 inches
Let's assume the length of the shorter section is x inches.
According to the problem, the length of the longer section is 5 inches longer than the shorter section, therefore it is x + 5 inches.
Twice the length of the longer section is three times the length of the shorter section, so:
2(x + 5) = 3x
Let's solve for x:
2x + 10 = 3x
10 = 3x - 2x
10 = x
Therefore, the length of the shorter section is 10 inches.
The correct answer is:
a. 10 inches
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You're welcome! I'm glad I could help. If you have any more questions, feel free to ask.
Let's denote the length of the shorter section of the string as x inches.
According to the given information, the longer section is 5 inches longer than the shorter section. So, the length of the longer section would be (x + 5) inches.
Twice the length of the longer section is three times the length of the shorter section. This can be written as the following equation:
2 * (x + 5) = 3 * x
Now, let's solve this equation to find the value of x:
2x + 10 = 3x
10 = 3x - 2x
10 = x
Therefore, the length of the shorter section is x = 10 inches.
So, the answer is option a) 10 inches.